General Mathematics - First Semester (1st Quarter)

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Which of the following represents the cost of hiring guides as a function of the number of tourists who wish to explore the cave?

f(x) = 4x

f(x) = 4 + x

f(x) = 4/x (correct)

f(x) = 4 - x

Which of the following represents the cost of renting a videoke machine as a piecewise function of the number of days it is rented?

f(x) = 1000 + 400(x-4)

f(x) = 1000 + 400(x-3) (correct)

f(x) = 1000 + 400x

f(x) = 1000x

What is the composition of functions f and g, (f∘g)(x)?

(f∘g)(x) = 1/x² - √x

(f∘g)(x) = 1/x² + √x

(f∘g)(x) = 1/(x+2) + (x-2)/x

(f∘g)(x) = 1/(x+2) - (x-2)/x (correct)

What is the composition of functions g and f, (g∘f)(x)?

(g∘f)(x) = 1/x² + √x Signup and view all the answers

What is the composition of functions f and f, (f∘f)(x)?

(f∘f)(x) = 1/(x²+4x+4)² Signup and view all the answers

Which of the following is a valid piecewise function representing the cost of renting a videoke machine for the given scenario?

$f(x) = 1000 + 400(x-3)$ Signup and view all the answers

Which of the following is the correct composition of functions f and g, $(f \circ g)(x)$?

$f(g(x)) = \frac{1}{(x+2)^2}$ Signup and view all the answers

Which of the following is the correct composition of functions f and f, $(f \circ f)(x)$?

$f(f(x)) = \frac{1}{x^2}$ Signup and view all the answers

Which of the following is a valid piecewise function representing the cost of renting a videoke machine for the given scenario?

$C(x) = 1000$ for $x \leq 3$, $C(x) = 1000 + 400(x-3)$ for $x > 3$ Signup and view all the answers

What is the composition of functions g and f, $(g \circ f)(x)$?

$(g \circ f)(x) = \frac{1},{(x+2)^2} - 2$ Signup and view all the answers

Which of the following represents the cost of hiring guides as a function of the number of tourists who wish to explore the cave?

$C(x) = 4x$ Signup and view all the answers

Which of the following is a characteristic of a rational function?

The function is in the form of f(x) = p(x)/q(x), where p(x) and q(x) are polynomial functions and q(x) ≠ 0. Signup and view all the answers

Which of the following is the correct form of a rational function?

f(x) = 2x + 4 / x^2 - 1 Signup and view all the answers

What is the domain of a rational function?

The set of real numbers except those values of x that make the denominator zero. Signup and view all the answers

What is an asymptote in a rational function?

A line that approaches the graph but never meets or intersects. Signup and view all the answers

What are intercepts in a rational function?

Points where the graph intersects both the x-axis and the y-axis. Signup and view all the answers

Which of the following is the correct form of a rational function?

$f(x) = \frac{p(x)}{q(x)}$ Signup and view all the answers

What is an asymptote in a rational function?

A line that approaches the graph but never meets or intersects. Signup and view all the answers

What is the domain of a rational function?

The set of real numbers except those values of x that will make the denominator zero. Signup and view all the answers

Which of the following is the correct form of a rational function?

$f(x) = \frac{x-4}{x-2}$ Signup and view all the answers

What is an asymptote in a rational function?

A line that approaches the graph but never meets or intersects Signup and view all the answers

What is the domain of a rational function?

The set of real numbers except those values of x that will make the denominator zero Signup and view all the answers

Which of the following is the correct equation to find the inverse of the function $f(x) = 1 + x - 2$?

$x - 1 = y - 2$ Signup and view all the answers

Which of the following is the correct equation for the inverse of the function $f(x) = \frac{x-2}{x+2}$?

$x = \frac{y-2}{y+2}$ Signup and view all the answers

What is the inverse of the function $f(x) = x^2 + x$?

$f^{-1}(x) = x^2 - x + 1$ Signup and view all the answers

What is the inverse of the function $f(x) = 1 - 4 - 3x$?

$f^{-1}(x) = 1 - 4 - 3x$ Signup and view all the answers

Which of the following statements about inverse functions is true?

Inverse functions have the same domain and range. Signup and view all the answers

Which of the following is the correct equation to find the inverse of the function $f(x) = rac{x-2}{x+2}$?

$f^{-1}(x) = rac{x+2}{x-2}$ Signup and view all the answers

Which of the following is the correct equation for the inverse of the function $f(x) = 1 + x - 2$?

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

Which of the following is the correct equation for the inverse of the function $f(x) = 1 - 4 - 3x$?

$f^{-1}(x) = rac{1 - x}{-3}$ Signup and view all the answers

Which of the following is the correct equation for the inverse of the function $f(x) = \frac{x-2},{x+2}$?

$f^{-1}(x) = \frac{x+2},{x-2}$ Signup and view all the answers

What is the domain of a rational function?

All real numbers except 0 Signup and view all the answers

Which of the following is the correct composition of functions $f$ and $g$, $(f \circ g)(x)$?

$f(g(x)) = 1 - 4 - 3x$ Signup and view all the answers

Which of the following is the correct exponential model for the situation?

$A(t) = 100e^{-rac{t}{250}}$ Signup and view all the answers

How much of the substance will remain after 500 years?

25g Signup and view all the answers

Which of the following is the correct exponential model for the situation?

$P(t) = 1000(3)^{rac{t}{80}}$ Signup and view all the answers

What is the size of the population after 100 years?

27,000 Signup and view all the answers

Which of the following is the correct exponential model for the situation?

$P(t) = 7000(1.12)^{t-2000}$ Signup and view all the answers

Which of the following is the correct exponential model for the situation when a substance with a half-life of 250 years initially has 100g?

$A(t) = 100 \cdot 2^{-\frac{t},{250}}$ Signup and view all the answers

How much of the substance will remain after 500 years if it initially had 100g and has a half-life of 250 years?

50g Signup and view all the answers

Which of the following is the correct exponential model for the situation when a population starts with 1,000 individuals and triples every 80 years?

$P(t) = 1000 \cdot 3^{\frac{t},{80}}$ Signup and view all the answers

Which of the following is the correct exponential model for the situation when a substance with a half-life of 250 years initially has 100g?

$A(t) = 100 \cdot \left(\frac{1},{2}\right)^{\frac{t},{250}}$ Signup and view all the answers

How much of the substance will remain after 500 years if it initially had 100g and has a half-life of 250 years?

50g Signup and view all the answers

Which of the following is the correct exponential model for the situation when a population starts with 1,000 individuals and triples every 80 years?

$P(t) = 1000 \cdot 3^{\frac{t},{80}}$ Signup and view all the answers

Which of the following is the correct equation for the inverse of the function $f(x) = rac{x-2}{x+2}$?

$f^{-1}(x) = rac{x+2}{x-2}$ Signup and view all the answers

Which of the following is the correct exponential model for the situation?

$y = ab^x$ Signup and view all the answers

What is an asymptote in a rational function?

A line that the graph of the function approaches but never touches. Signup and view all the answers

What is the domain of a rational function?

The set of all real numbers except for the values that make the denominator zero. Signup and view all the answers

How much of the substance will remain after 500 years if it initially had 100g and has a half-life of 250 years?

50g Signup and view all the answers

Which of the following is the correct logarithmic form for the exponential equation $5^2 = 25$?

$\log_5 25 = 2$ Signup and view all the answers

Which of the following is the correct logarithmic form for the exponential equation $2^3 = 8$?

$\log_2 8 = 3$ Signup and view all the answers

Which of the following is the correct logarithmic form for the exponential equation $10^2 = 100$?

$\log_{10} 100 = 2$ Signup and view all the answers

Which of the following is the correct logarithmic form for the exponential equation $10^2 = 100$?

$log_{10} 100 = 2$ Signup and view all the answers

What is the domain of a logarithmic function?

All positive real numbers Signup and view all the answers

Which of the following is the correct equation for the inverse of the function $f(x) = \frac{1},{x}$?

$f^{-1}(x) = \frac{1},{x}$ Signup and view all the answers

Which equation represents the solution to the logarithmic equation log2(x) = log2(14)?

x = 14 Signup and view all the answers

What is the solution to the logarithmic equation logb(x - 30) = logb(x)?

x = 30 Signup and view all the answers

What is the solution to the logarithmic equation 2logb(4) + logb(x - 1) = 3?

x = 4 Signup and view all the answers

Which inequality represents the solution to the logarithmic inequality log3(2x - 1) > log3(x + 2)?

x > 3 Signup and view all the answers

Which equation represents the solution to the logarithmic equation log2(8) = x?

x = 2 Signup and view all the answers

Which of the following is the solution to the equation logb x^2 = logb(4x - 4)?

x = 4 Signup and view all the answers

Which of the following is the solution to the equation log2(2x - 1) = 2?

x = 3 Signup and view all the answers

Which of the following is the solution to the inequality log3(2x - 1) > log3(x + 2)?

x > 3 Signup and view all the answers

Which of the following is the solution to the equation $log_2(x) = log_2(14)$?

x = 14 Signup and view all the answers

What is the solution to the logarithmic equation $log_b(x - 30) = log_b(x)$?

x = 30 Signup and view all the answers

Which of the following is the correct solution to the equation $2log_b 4 + log_b(x - 1) = 3$?

x = 6 Signup and view all the answers

General Mathematics - First Semester (1st Quarter)

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Questions and Answers

Which of the following represents the cost of hiring guides as a function of the number of tourists who wish to explore the cave?

Which of the following represents the cost of renting a videoke machine as a piecewise function of the number of days it is rented?

What is the composition of functions f and g, (f∘g)(x)?

What is the composition of functions g and f, (g∘f)(x)?

What is the composition of functions f and f, (f∘f)(x)?

Which of the following is a valid piecewise function representing the cost of renting a videoke machine for the given scenario?

Which of the following is the correct composition of functions f and g, $(f \circ g)(x)$?

Which of the following is the correct composition of functions f and f, $(f \circ f)(x)$?

Which of the following is a valid piecewise function representing the cost of renting a videoke machine for the given scenario?

What is the composition of functions g and f, $(g \circ f)(x)$?

Which of the following represents the cost of hiring guides as a function of the number of tourists who wish to explore the cave?

Which of the following is a characteristic of a rational function?

Which of the following is the correct form of a rational function?

What is the domain of a rational function?

What is an asymptote in a rational function?

What are intercepts in a rational function?

Which of the following is the correct form of a rational function?

What is an asymptote in a rational function?

What is the domain of a rational function?

Which of the following is the correct form of a rational function?

What is an asymptote in a rational function?

What is the domain of a rational function?

Which of the following is the correct equation to find the inverse of the function $f(x) = 1 + x - 2$?

Which of the following is the correct equation for the inverse of the function $f(x) = \frac{x-2}{x+2}$?

What is the inverse of the function $f(x) = x^2 + x$?

What is the inverse of the function $f(x) = 1 - 4 - 3x$?

Which of the following statements about inverse functions is true?

Which of the following is the correct equation to find the inverse of the function $f(x) = rac{x-2}{x+2}$?

Which of the following is the correct equation for the inverse of the function $f(x) = 1 + x - 2$?

Which of the following is the correct equation for the inverse of the function $f(x) = 1 - 4 - 3x$?

Which of the following is the correct equation for the inverse of the function $f(x) = \frac{x-2},{x+2}$?

What is the domain of a rational function?

Which of the following is the correct composition of functions $f$ and $g$, $(f \circ g)(x)$?

Which of the following is the correct exponential model for the situation?

How much of the substance will remain after 500 years?

Which of the following is the correct exponential model for the situation?

What is the size of the population after 100 years?

Which of the following is the correct exponential model for the situation?

Which of the following is the correct exponential model for the situation when a substance with a half-life of 250 years initially has 100g?

How much of the substance will remain after 500 years if it initially had 100g and has a half-life of 250 years?

Which of the following is the correct exponential model for the situation when a population starts with 1,000 individuals and triples every 80 years?

Which of the following is the correct exponential model for the situation when a substance with a half-life of 250 years initially has 100g?

How much of the substance will remain after 500 years if it initially had 100g and has a half-life of 250 years?

Which of the following is the correct exponential model for the situation when a population starts with 1,000 individuals and triples every 80 years?

Which of the following is the correct equation for the inverse of the function $f(x) = rac{x-2}{x+2}$?

Which of the following is the correct exponential model for the situation?

What is an asymptote in a rational function?

What is the domain of a rational function?

How much of the substance will remain after 500 years if it initially had 100g and has a half-life of 250 years?

Which of the following is the correct logarithmic form for the exponential equation $5^2 = 25$?

Which of the following is the correct logarithmic form for the exponential equation $2^3 = 8$?

Which of the following is the correct logarithmic form for the exponential equation $10^2 = 100$?

Which of the following is the correct logarithmic form for the exponential equation $10^2 = 100$?

What is the domain of a logarithmic function?

Which of the following is the correct equation for the inverse of the function $f(x) = \frac{1},{x}$?

Which equation represents the solution to the logarithmic equation log2(x) = log2(14)?

What is the solution to the logarithmic equation logb(x - 30) = logb(x)?

What is the solution to the logarithmic equation 2logb(4) + logb(x - 1) = 3?

Which inequality represents the solution to the logarithmic inequality log3(2x - 1) > log3(x + 2)?

Which equation represents the solution to the logarithmic equation log2(8) = x?

Which of the following is the solution to the equation logb x^2 = logb(4x - 4)?

Which of the following is the solution to the equation log2(2x - 1) = 2?

Which of the following is the solution to the inequality log3(2x - 1) > log3(x + 2)?

Which of the following is the solution to the equation $log_2(x) = log_2(14)$?

What is the solution to the logarithmic equation $log_b(x - 30) = log_b(x)$?

Which of the following is the correct solution to the equation $2log_b 4 + log_b(x - 1) = 3$?

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