Gr12 Mathematics: Ch 2 Sum Functions

What is a key characteristic of a relation?

There are no elements in set A or set B.
Each element in set A is associated with exactly one element in set B.
Each element in set B can map to multiple elements in set A.
Each element in set A can map to multiple elements in set B. (correct)

What is the graphical representation of a one-to-one function?

Every vertical line intersects the graph at most once. (correct)
Every horizontal line intersects the graph at most once.
Every horizontal line intersects the graph more than once.
Every vertical line intersects the graph more than once.

What is the definition of an inverse function?

An inverse function is the same as the original function.
An inverse function reverses the operation of a given function. (correct)
An inverse function is the square of the original function.
An inverse function is the reciprocal of the original function.

What is a requirement for a function to have an inverse?

The function must be one-to-one. (A) Signup and view all the answers

What is the graphical representation of the inverse function?

The graph of the inverse function is the reflection of the original function's graph across the line y = x. (A) Signup and view all the answers

How do you find the inverse function?

Interchange x and y in the equation y = f(x) and solve for x. (B) Signup and view all the answers

What type of function has multiple elements of the domain mapping to the same element of the range?

Many-to-one function. (D) Signup and view all the answers

What is an example of a function that is not one-to-one?

A constant function with multiple outputs. (A) Signup and view all the answers

What is the horizontal asymptote of an exponential function y = b^x?

y = 0 (A) Signup and view all the answers

What is the logarithmic equivalent of the exponential equation 2^3 = 8?

log_2 8 = 3 (A) Signup and view all the answers

What is the value of log_a a?

1 (D) Signup and view all the answers

What is the product rule of logarithms?

log_a(xy) = log_a x + log_a y (B) Signup and view all the answers

What is the range of a logarithmic function y = log_b x?

y ∈ ℝ (C) Signup and view all the answers

What is the application of logarithms in finance?

Calculating loan repayments and interest rates (B) Signup and view all the answers

What is the graph of the inverse of an exponential function?

Reflection about the line y = x (D) Signup and view all the answers

What is the formula to convert from exponential to logarithmic form?

log_b x = b^x (A) Signup and view all the answers

What is the graphical representation of f(x) and f^(-1)(x)?

Symmetrical about the line y = x (A) Signup and view all the answers

What is the notation f^(-1)(x) indicating?

The inverse function of f(x) (C) Signup and view all the answers

What is the condition for a function to have an inverse that is also a function?

One-to-one (C) Signup and view all the answers

What is the inverse of a linear function f(x) = ax + q?

f^(-1)(x) = (1/a)x - (q/a) (B) Signup and view all the answers

What is the domain and range of the inverse function of a linear function f(x) = ax + q?

Domain: R, Range: R (C) Signup and view all the answers

What is the general form of the inverse of a quadratic function y = ax^2?

y = ±√(x/a) (A) Signup and view all the answers

What is the restriction on the domain of the quadratic function y = ax^2 for its inverse to be a function?

x ≥ 0 if a > 0, x ≤ 0 if a < 0 (B) Signup and view all the answers

What is the graph of the exponential function f(x) = b^x like if b > 1?

The graph rises rapidly (A) Signup and view all the answers

What is the inverse of the exponential function y = b^x?

y = log_b(x) (D) Signup and view all the answers

What is the definition of a logarithm?

The exponent to which a base must be raised to yield a number (A) Signup and view all the answers

Which type of function has a unique output for every input?

One-to-One Function (A) Signup and view all the answers

What is the purpose of an inverse function?

To reverse the operation of a given function (C) Signup and view all the answers

What is a necessary condition for a function to have an inverse?

The function must be one-to-one (C) Signup and view all the answers

What is the graphical representation of the inverse function?

The reflection of the original function's graph across the line y = x (D) Signup and view all the answers

If a function f(x) is one-to-one, what can be said about its inverse f⁻¹(y)?

It is a one-to-one function (C) Signup and view all the answers

What is the first step to find the inverse function f⁻¹(y)?

Interchange x and y in the equation f(x) = y (B) Signup and view all the answers

What type of relation has a single element in set A mapping to multiple elements in set B?

One-to-Many Relation (C) Signup and view all the answers

Which of the following statements is true about functions?

All functions are relations (D) Signup and view all the answers

What is the exponential equivalent of the logarithmic equation log₂ 128 = 7?

2⁷ = 128 (A) Signup and view all the answers

What is the shape of the graph of the logarithmic function y = log_b x?

Increasing (C) Signup and view all the answers

What is the domain of the exponential function y = b^x?

x ∈ ℝ (B) Signup and view all the answers

What is the purpose of the change of base formula in logarithms?

To convert between different bases (D) Signup and view all the answers

What is the application of logarithms in the context of population growth?

To calculate the rate of growth (B) Signup and view all the answers

What is the graph of the inverse of an exponential function similar to?

A reflection about the line y = x (B) Signup and view all the answers

What is the property of logarithms that states log_a(xy) = log_a x + log_a y?

Product rule (A) Signup and view all the answers

What is the formula to calculate the pH level of a solution?

pH = -log₁₀[H⁺] (D) Signup and view all the answers

What is the inverse of the linear function f(x) = 2x + 3?

f^{-1}(x) = (1/2)x - (3/2) (B) Signup and view all the answers

What is the domain of the inverse function of y = ax^2, assuming a > 0?

x ≥ 0 (C) Signup and view all the answers

What is the graphical representation of f(x) and f^{-1}(x)?

F(x) and f^{-1}(x) are symmetrical about the line y = x (C) Signup and view all the answers

What is the inverse of the exponential function y = 2^x?

y = log2(x) (B) Signup and view all the answers

What is the general form of a quadratic function?

y = ax^2 + q (C) Signup and view all the answers

What is the range of the inverse function of a linear function f(x) = ax + q?

All real numbers (B) Signup and view all the answers

What is the restriction on the domain of the quadratic function y = ax^2 for its inverse to be a function, assuming a > 0?

x ≥ 0 (D) Signup and view all the answers

What is the definition of a logarithm?

The logarithm is the exponent to which a base must be raised to yield a number (A) Signup and view all the answers

What is the graph of the exponential function f(x) = 2^x like if 0 < 2 < 1?

The function is decreasing (D) Signup and view all the answers

What is the condition for a function to have an inverse that is also a function?

The function must be one-to-one (D) Signup and view all the answers

What is the primary difference between a function and a relation?

A function has a unique output for every input, while a relation may have multiple outputs for an input. (B) Signup and view all the answers

If a function f(x) is one-to-one, what can be said about its inverse f⁻¹(y)?

The inverse function is also one-to-one. (C) Signup and view all the answers

What is the graphical representation of a many-to-one function?

Different vertical lines can intersect the graph at the same y-value. (A) Signup and view all the answers

What is a necessary condition for a function to have an inverse that is also a function?

The function must be one-to-one. (D) Signup and view all the answers

What is the purpose of finding the inverse of a function?

To reverse the operation of the function. (D) Signup and view all the answers

What is the reflection of the graph of the inverse function with respect to the original function?

The line y = x. (D) Signup and view all the answers

What type of function has a unique output for every input?

One-to-one function. (B) Signup and view all the answers

What is the first step to find the inverse function f⁻¹(y)?

Interchange x and y in the equation y = f(x). (D) Signup and view all the answers

What happens to the domain and range of a function when its inverse is found?

The domain and range are swapped. (B) Signup and view all the answers

What is the purpose of restricting the domain of a quadratic function so that its inverse can be a function?

To make the function one-to-one. (C) Signup and view all the answers

What is the effect of interchanging x and y in the equation of a function?

It results in the inverse function. (C) Signup and view all the answers

What is the graphical representation of the inverse of a linear function?

A reflection about the line y = x. (C) Signup and view all the answers

What is the condition for a function to have an inverse that is also a function?

The function must be one-to-one. (A) Signup and view all the answers

What is the formula for finding the inverse of a linear function f(x) = ax + q?

f^(-1)(x) = x/a - q/a. (D) Signup and view all the answers

What is the graphical representation of the inverse of an exponential function?

A logarithmic curve. (A) Signup and view all the answers

What is the purpose of finding the inverse of a function?

To reverse the operation of the function. (C) Signup and view all the answers

What is the definition of a logarithm?

The logarithm of a number x with a base b is the exponent y to which b must be raised to yield x. (C) Signup and view all the answers

What is the graphical representation of the exponential function f(x) = b^x?

A rapidly increasing or decreasing curve. (A) Signup and view all the answers

What is the correct logarithmic equivalent of the exponential equation 3^4 = 81?

log₃ 81 = 4 (A) Signup and view all the answers

What is the value of log₅ (√5) in simplest form?

1/2 (B) Signup and view all the answers

What is the graph of the logarithmic function y = log₂ x similar to?

A curve that is asymptotic to the y-axis (C) Signup and view all the answers

If a population doubles in size every 5 years, what is the formula to model this growth?

A = P(2)^n (B) Signup and view all the answers

What is the correct formula to convert from exponential to logarithmic form?

log_b x = b^x (B) Signup and view all the answers

What is the purpose of the change of base formula in logarithms?

To evaluate logarithms with different bases (A) Signup and view all the answers

What is the range of the logarithmic function y = log_b x?

y ∈ ℝ (B) Signup and view all the answers

Which of the following is an application of logarithms in science?

Modeling population growth (B) Signup and view all the answers

What is the necessary condition for a function to have an inverse that is also a function?

The function is one-to-one. (D) Signup and view all the answers

If a function f(x) is many-to-one, what can be said about its inverse f⁻¹(y)?

It is not a function. (B) Signup and view all the answers

What is the graphical representation of a one-to-one function and its inverse?

They are reflections of each other across the line y = x. (D) Signup and view all the answers

What type of function has a unique output for every input, and every output corresponds to exactly one input?

One-to-one function. (C) Signup and view all the answers

What is the purpose of an inverse function?

To undo the operation of the original function. (D) Signup and view all the answers

Which type of relation has a single element in set A mapping to multiple elements in set B?

One-to-many relation. (C) Signup and view all the answers

What is the result of interchanging x and y in the equation y = f(x) when finding the inverse function?

x = f⁻¹(y). (A) Signup and view all the answers

What is a characteristic of a one-to-one function?

Every vertical line intersects the graph at most once. (D) Signup and view all the answers

What is the graphical representation of the inverse of an exponential function y = b^x?

A reflection of the original function about the line y = x (D) Signup and view all the answers

What is the purpose of the change of base formula in logarithms?

To convert between different logarithmic bases (A) Signup and view all the answers

What is the application of logarithms in the context of population growth?

To model population growth (A) Signup and view all the answers

What is the property of logarithms that states log_a(xy) = log_a x + log_a y?

Product rule (B) Signup and view all the answers

What is the formula to calculate the pH level of a solution?

pH = -log[H^+] (C) Signup and view all the answers

What is the range of the inverse function of a logarithmic function y = log_b x?

y ∈ ℝ (D) Signup and view all the answers

What is the graphical representation of the logarithmic function y = log_b x?

An increasing curve with a vertical asymptote at x = 0 (B) Signup and view all the answers

What is the logarithmic equivalent of the exponential equation 2^3 = 8?

log_2 8 = 3 (A) Signup and view all the answers

What is the correct method to find the inverse of a linear function f(x) = ax + q?

Interchange x and y in the equation y = ax + q, and then solve for y. (D) Signup and view all the answers

What is the correct formula for the inverse of the quadratic function y = ax^2?

y = ±√(x/a) (C) Signup and view all the answers

What is the relationship between the domain and range of a function and its inverse?

The domain of the function becomes the range of the inverse, and the range of the function becomes the domain of the inverse. (A) Signup and view all the answers

What is the graphical representation of the inverse of an exponential function y = b^x?

A reflection about the line y = x. (D) Signup and view all the answers

What is the correct statement about the inverse of a quadratic function y = ax^2?

The inverse is a function if the domain is restricted. (D) Signup and view all the answers

What is the property of logarithms that states log_b(xy) = log_b x + log_b y?

Product rule (D) Signup and view all the answers

What is the correct formula for the inverse of the exponential function y = b^x?

y = log_b x (A) Signup and view all the answers

What is the restriction on the domain of the quadratic function y = ax^2 for its inverse to be a function?

x ≥ 0 if a > 0, and x ≤ 0 if a < 0 (C) Signup and view all the answers

What is the graphical representation of the exponential function y = b^x if b > 1?

A rapidly rising curved line (D) Signup and view all the answers

What is the definition of a logarithm?

The exponent to which a base must be raised to yield a given value. (A) Signup and view all the answers

Gr12 Mathematics: Ch 2 Sum Functions

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Questions and Answers

What is a key characteristic of a relation?

What is the graphical representation of a one-to-one function?

What is the definition of an inverse function?

What is a requirement for a function to have an inverse?

What is the graphical representation of the inverse function?

How do you find the inverse function?

What type of function has multiple elements of the domain mapping to the same element of the range?

What is an example of a function that is not one-to-one?

What is the horizontal asymptote of an exponential function y = b^x?

What is the logarithmic equivalent of the exponential equation 2^3 = 8?

What is the value of log_a a?

What is the product rule of logarithms?

What is the range of a logarithmic function y = log_b x?

What is the application of logarithms in finance?

What is the graph of the inverse of an exponential function?

What is the formula to convert from exponential to logarithmic form?

What is the graphical representation of f(x) and f^(-1)(x)?

What is the notation f^(-1)(x) indicating?

What is the condition for a function to have an inverse that is also a function?

What is the inverse of a linear function f(x) = ax + q?

What is the domain and range of the inverse function of a linear function f(x) = ax + q?

What is the general form of the inverse of a quadratic function y = ax^2?

What is the restriction on the domain of the quadratic function y = ax^2 for its inverse to be a function?

What is the graph of the exponential function f(x) = b^x like if b > 1?

What is the inverse of the exponential function y = b^x?

What is the definition of a logarithm?

Which type of function has a unique output for every input?

What is the purpose of an inverse function?

What is a necessary condition for a function to have an inverse?

What is the graphical representation of the inverse function?

If a function f(x) is one-to-one, what can be said about its inverse f⁻¹(y)?

What is the first step to find the inverse function f⁻¹(y)?

What type of relation has a single element in set A mapping to multiple elements in set B?

Which of the following statements is true about functions?

What is the exponential equivalent of the logarithmic equation log₂ 128 = 7?

What is the shape of the graph of the logarithmic function y = log_b x?

What is the domain of the exponential function y = b^x?

What is the purpose of the change of base formula in logarithms?

What is the application of logarithms in the context of population growth?

What is the graph of the inverse of an exponential function similar to?

What is the property of logarithms that states log_a(xy) = log_a x + log_a y?

What is the formula to calculate the pH level of a solution?

What is the inverse of the linear function f(x) = 2x + 3?

What is the domain of the inverse function of y = ax^2, assuming a > 0?

What is the graphical representation of f(x) and f^{-1}(x)?

What is the inverse of the exponential function y = 2^x?

What is the general form of a quadratic function?

What is the range of the inverse function of a linear function f(x) = ax + q?

What is the restriction on the domain of the quadratic function y = ax^2 for its inverse to be a function, assuming a > 0?

What is the definition of a logarithm?

What is the graph of the exponential function f(x) = 2^x like if 0 < 2 < 1?

What is the condition for a function to have an inverse that is also a function?

What is the primary difference between a function and a relation?

If a function f(x) is one-to-one, what can be said about its inverse f⁻¹(y)?

What is the graphical representation of a many-to-one function?

What is a necessary condition for a function to have an inverse that is also a function?

What is the purpose of finding the inverse of a function?

What is the reflection of the graph of the inverse function with respect to the original function?

What type of function has a unique output for every input?

What is the first step to find the inverse function f⁻¹(y)?

What happens to the domain and range of a function when its inverse is found?

What is the purpose of restricting the domain of a quadratic function so that its inverse can be a function?

What is the effect of interchanging x and y in the equation of a function?

What is the graphical representation of the inverse of a linear function?

What is the condition for a function to have an inverse that is also a function?

What is the formula for finding the inverse of a linear function f(x) = ax + q?

What is the graphical representation of the inverse of an exponential function?

What is the purpose of finding the inverse of a function?

What is the definition of a logarithm?

What is the graphical representation of the exponential function f(x) = b^x?

What is the correct logarithmic equivalent of the exponential equation 3^4 = 81?

What is the value of log₅ (√5) in simplest form?

What is the graph of the logarithmic function y = log₂ x similar to?

If a population doubles in size every 5 years, what is the formula to model this growth?

What is the correct formula to convert from exponential to logarithmic form?

What is the purpose of the change of base formula in logarithms?