Question 1

Given the graph of $$y = f(x)$$ shown in Image 1 (the downward-opening parabola), which of the following best describes the domain and range of the function?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, 4]$$

Question 2

Refer to Image 2 (the line segment from $$(-3, 1) to$$ $$(2, 2)). $$What is the average rate of change of $$f(x)$$ from $$x = -3 to$$ $$x = 2$$?

Accepted Answer

$$\frac{2 - 1}{2 - (-3)} = \frac{1}{5}$$

Question 3

Which of the following equations represents a function whose graph passes the vertical line test?

Accepted Answer

$$y = x^2$ + 1$$

Question 4

Given the function $$f(x) = 6x^2$ + 2x + 1$$, what is the simplified form of the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$12x + 2 + 6h$$

Question 5

Which of the following functions is even?

Accepted Answer

$$h(x) = 2x^2$ + x^4$ + 3$$

Question 6

A line passes through the points $$(9, -44)$$ and $$(-6, 16). $$What is the slope of the line?

Accepted Answer

$$m = \frac{16 - (-44)}{-6 - 9} = -4$$

Question 7

Which of the following lines is perpendicular to $$y = 2x + 3$$?

Accepted Answer

$$y = -\frac{1}{2}x + 1$$

Question 8

Given $$f(x) = x - 6$$ and $$g(x) = 5x^2$, what is the domain of $$\frac{f}{g}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 9

If $$f(x) = 2x - 4$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 4}{2}$$

Question 10

What is the standard form of the equation of a circle with center $$(2, -1)$$ and radius $$r = \sqrt{5}$$?

Accepted Answer

$$(x - 2)^2$ + (y + 1)^2$ = 5$$

Question 11

Given the function $$f(x) = \sqrt{x + 2}$$, what is the domain of $$f$$?

Accepted Answer

$$[-2, \infty)$$

Question 12

Which transformation describes $$g(x) = 2f(x - 1)$$ compared to $$f(x)$$?

Accepted Answer

Horizontal shift right by 1 unit and vertical stretch by a factor of 2

Question 13

If $$f(x) = 7x + 1$$ and $$g(x) = 2x^2$ - 9$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$f(g(x)) = 7(2x^2$ - 9) + 1 = 14x^2$ - 62$$

Question 14

Which of the following best describes the symmetry of the function $$f(x) = x^3$ - x$$?

Accepted Answer

Odd function; symmetric about the origin

Question 15

Given the endpoints $$(2, -4)$$ and $$(-1, 5)$$, what is the distance between the points?

Accepted Answer

$$\sqrt{(2 - (-1))^2$ + ((-4) - 5)^2$} = \sqrt{9 + 81} = 3\sqrt{10}$$

Question 16

Which of the following is the general form of the equation of a line?

Accepted Answer

$$Ax + By + C = 0$$

Question 17

If $$f(x) = x^2$ + x - 12$$, what is the domain of $$f$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 18

A circle has the equation $$(x + 2)^2$ + (y - 3)^2$ = 4. $$What is the center and radius of the circle?

Accepted Answer

Center: $$(-2, 3)$$, Radius: $$2$$

College Algebra Chapter 2: Functions and Their Graphs

Study Guide - Practice Questions

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