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Gr12 Mathematics: Ch 2 Sum Functions
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Gr12 Mathematics: Ch 2 Sum Functions

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@TalentedParody

Questions and Answers

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?

    <p>The function must be one-to-one.</p> Signup and view all the answers

    What is the graphical representation of the inverse function?

    <p>The graph of the inverse function is the reflection of the original function's graph across the line y = x.</p> Signup and view all the answers

    How do you find the inverse function?

    <p>Interchange x and y in the equation y = f(x) and solve for x.</p> Signup and view all the answers

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

    <p>Many-to-one function.</p> Signup and view all the answers

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

    <p>A constant function with multiple outputs.</p> Signup and view all the answers

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

    <p>y = 0</p> Signup and view all the answers

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

    <p>log_2 8 = 3</p> Signup and view all the answers

    What is the value of log_a a?

    <p>1</p> Signup and view all the answers

    What is the product rule of logarithms?

    <p>log_a(xy) = log_a x + log_a y</p> Signup and view all the answers

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

    <p>y ∈ ℝ</p> Signup and view all the answers

    What is the application of logarithms in finance?

    <p>Calculating loan repayments and interest rates</p> Signup and view all the answers

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

    <p>Reflection about the line y = x</p> Signup and view all the answers

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

    <p>log_b x = b^x</p> Signup and view all the answers

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

    <p>Symmetrical about the line y = x</p> Signup and view all the answers

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

    <p>The inverse function of f(x)</p> Signup and view all the answers

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

    <p>One-to-one</p> Signup and view all the answers

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

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

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

    <p>Domain: R, Range: R</p> Signup and view all the answers

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

    <p>y = ±√(x/a)</p> 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?

    <p>x ≥ 0 if a &gt; 0, x ≤ 0 if a &lt; 0</p> Signup and view all the answers

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

    <p>The graph rises rapidly</p> Signup and view all the answers

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

    <p>y = log_b(x)</p> Signup and view all the answers

    What is the definition of a logarithm?

    <p>The exponent to which a base must be raised to yield a number</p> Signup and view all the answers

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

    <p>One-to-One Function</p> Signup and view all the answers

    What is the purpose of an inverse function?

    <p>To reverse the operation of a given function</p> Signup and view all the answers

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

    <p>The function must be one-to-one</p> Signup and view all the answers

    What is the graphical representation of the inverse function?

    <p>The reflection of the original function's graph across the line y = x</p> 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)?

    <p>It is a one-to-one function</p> Signup and view all the answers

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

    <p>Interchange x and y in the equation f(x) = y</p> Signup and view all the answers

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

    <p>One-to-Many Relation</p> Signup and view all the answers

    Which of the following statements is true about functions?

    <p>All functions are relations</p> Signup and view all the answers

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

    <p>2⁷ = 128</p> Signup and view all the answers

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

    <p>Increasing</p> Signup and view all the answers

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

    <p>x ∈ ℝ</p> Signup and view all the answers

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

    <p>To convert between different bases</p> Signup and view all the answers

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

    <p>To calculate the rate of growth</p> Signup and view all the answers

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

    <p>A reflection about the line y = x</p> Signup and view all the answers

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

    <p>Product rule</p> Signup and view all the answers

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

    <p>pH = -log₁₀[H⁺]</p> Signup and view all the answers

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

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

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

    <p>x ≥ 0</p> Signup and view all the answers

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

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

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

    <p>y = log2(x)</p> Signup and view all the answers

    What is the general form of a quadratic function?

    <p>y = ax^2 + q</p> Signup and view all the answers

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

    <p>All real numbers</p> 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?

    <p>x ≥ 0</p> Signup and view all the answers

    What is the definition of a logarithm?

    <p>The logarithm is the exponent to which a base must be raised to yield a number</p> Signup and view all the answers

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

    <p>The function is decreasing</p> Signup and view all the answers

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

    <p>The function must be one-to-one</p> Signup and view all the answers

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

    <p>A function has a unique output for every input, while a relation may have multiple outputs for an input.</p> 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)?

    <p>The inverse function is also one-to-one.</p> Signup and view all the answers

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

    <p>Different vertical lines can intersect the graph at the same y-value.</p> Signup and view all the answers

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

    <p>The function must be one-to-one.</p> Signup and view all the answers

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

    <p>To reverse the operation of the function.</p> Signup and view all the answers

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

    <p>The line y = x.</p> Signup and view all the answers

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

    <p>One-to-one function.</p> Signup and view all the answers

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

    <p>Interchange x and y in the equation y = f(x).</p> Signup and view all the answers

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

    <p>The domain and range are swapped.</p> 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?

    <p>To make the function one-to-one.</p> Signup and view all the answers

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

    <p>It results in the inverse function.</p> Signup and view all the answers

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

    <p>A reflection about the line y = x.</p> Signup and view all the answers

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

    <p>The function must be one-to-one.</p> Signup and view all the answers

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

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

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

    <p>A logarithmic curve.</p> Signup and view all the answers

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

    <p>To reverse the operation of the function.</p> Signup and view all the answers

    What is the definition of a logarithm?

    <p>The logarithm of a number x with a base b is the exponent y to which b must be raised to yield x.</p> Signup and view all the answers

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

    <p>A rapidly increasing or decreasing curve.</p> Signup and view all the answers

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

    <p>log₃ 81 = 4</p> Signup and view all the answers

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

    <p>1/2</p> Signup and view all the answers

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

    <p>A curve that is asymptotic to the y-axis</p> Signup and view all the answers

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

    <p>A = P(2)^n</p> Signup and view all the answers

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

    <p>log_b x = b^x</p> Signup and view all the answers

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

    <p>To evaluate logarithms with different bases</p> Signup and view all the answers

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

    <p>y ∈ ℝ</p> Signup and view all the answers

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

    <p>Modeling population growth</p> Signup and view all the answers

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

    <p>The function is one-to-one.</p> 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)?

    <p>It is not a function.</p> Signup and view all the answers

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

    <p>They are reflections of each other across the line y = x.</p> 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?

    <p>One-to-one function.</p> Signup and view all the answers

    What is the purpose of an inverse function?

    <p>To undo the operation of the original function.</p> Signup and view all the answers

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

    <p>One-to-many relation.</p> 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?

    <p>x = f⁻¹(y).</p> Signup and view all the answers

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

    <p>Every vertical line intersects the graph at most once.</p> Signup and view all the answers

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

    <p>A reflection of the original function about the line y = x</p> Signup and view all the answers

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

    <p>To convert between different logarithmic bases</p> Signup and view all the answers

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

    <p>To model population growth</p> Signup and view all the answers

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

    <p>Product rule</p> Signup and view all the answers

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

    <p>pH = -log[H^+]</p> Signup and view all the answers

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

    <p>y ∈ ℝ</p> Signup and view all the answers

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

    <p>An increasing curve with a vertical asymptote at x = 0</p> Signup and view all the answers

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

    <p>log_2 8 = 3</p> Signup and view all the answers

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

    <p>Interchange x and y in the equation y = ax + q, and then solve for y.</p> Signup and view all the answers

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

    <p>y = ±√(x/a)</p> Signup and view all the answers

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

    <p>The domain of the function becomes the range of the inverse, and the range of the function becomes the domain of the inverse.</p> Signup and view all the answers

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

    <p>A reflection about the line y = x.</p> Signup and view all the answers

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

    <p>The inverse is a function if the domain is restricted.</p> Signup and view all the answers

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

    <p>Product rule</p> Signup and view all the answers

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

    <p>y = log_b x</p> 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?

    <p>x ≥ 0 if a &gt; 0, and x ≤ 0 if a &lt; 0</p> Signup and view all the answers

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

    <p>A rapidly rising curved line</p> Signup and view all the answers

    What is the definition of a logarithm?

    <p>The exponent to which a base must be raised to yield a given value.</p> Signup and view all the answers

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