Question 1

Given the points (2, 4) and (3, 7), which of the following equations represents the line passing through these points?

Accepted Answer

$$y = 3x - 2$$

Question 2

Which graph correctly represents the line passing through the points (2, 4) and (3, 7) with the equation $$y = 3x - 2$$?

Accepted Answer

Image 1

Question 3

The greatest-integer function $$f(x) = \lfloor x \rfloor$$ for $$-2 \leq x \leq 2 is $$best represented by which graph?

Accepted Answer

Image 5

Question 4

Given $$f(x) = 3x^2$ + 2$$ for $$x \geq 0$$, which of the following is the correct inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt{\frac{x-2}{3}}$$

Question 5

Which graph best represents both $$f(x) = 3x^2$ + 2$$ and its inverse $$f^{-1}(x$$) = \sqrt{\frac{x-2}{3}}$$?

Accepted Answer

Image 9

Question 6

Given $$g(x) = 2\ln(x-3) + 4$$, which of the following is the correct inverse function $$g^{-1}(x$$)$$?

Accepted Answer

$$g^{-1}(x$$) = $$e^{\frac{x-4}$${2}} + 3$$

Question 7

If a function $$h(x) is $$one-to-one and its graph passes the horizontal line test, which of the following statements is true?

Accepted Answer

The function has an inverse that is also a function.

Question 8

A real-world application: The temperature $$T in $$Celsius is related to Fahrenheit $$F by$$ $$F = \frac{9}{5}C + 32. $$What is the inverse function to convert Fahrenheit to Celsius?

Accepted Answer

$$C = \frac{5}{9}(F - 32)$$

Question 9

Suppose $$f(x) is an $$even function. Which of the following must be true for all $$x in $$the domain of $$f$$?

Accepted Answer

$$f(-x) = f(x)$$

Question 10

A pharmaceutical company models the concentration $$C of a $$drug in the bloodstream $$t$$ hours after administration by $$C(t) = 10e$$^{-0.5t}$$. What is the initial concentration?

Accepted Answer

$$10$$

Question 11

Which of the following statements about the greatest-integer function $$f(x) = \lfloor x \rfloor is $$correct?

Accepted Answer

It returns the greatest integer less than or equal to $$x.$$

Question 12

If $$f(x) = 2x + 5$$ and $$g(x) = x^2$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$2x^2 + 5$

Question 13

Which of the following is the domain of the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

$$x \geq 2$$

Question 14

A population of bacteria doubles every 3 hours. If the initial population is $$P_0$$, which function models the population after $$t$$ hours?

Accepted Answer

$$P(t) = P_0$ \cdot 2$$^{t/3}$$

Question 15

If $$f(x) is $$invertible and $$f(2) = 5$$, what is $$f^{-1}(5$$)$$?

Accepted Answer

$$2$$

Question 16

Which of the following is NOT a property of logarithmic functions?

Accepted Answer

$$\log(a + b) = \log a + \log b$$

Study Guide: Common Functions and Their Properties

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