Q: Given $$f(x) = \frac{2x}{x^2$ - 2}$$ and $$g(x) = \frac{2x + 3}{x}$$, are $$f$$ and $$g$$ inverses of each other?

No, because $$f(g(x)) \neq x$$ for all $$x in $$the domain.

Question 1

Given the function $$f(x) = x^2$ - 2x - 7$$, what is the value of $$f(3)$$?

Accepted Answer

$$-4$$

Question 2

Which of the following sets of points represents the graph of a function?

Accepted Answer

$$\{(-1, 4), (2, -1), (6, -5), (8, 3), (10, 3)\}$$

Question 3

How can the graph of $$f(x) = -\sqrt{x - 4} be $$obtained from the graph of $$y = \sqrt{x}$$?

Accepted Answer

Shift 4 units to the right and reflect across the $$x-$$axis.

Question 4

Given $$f(x) = 2x^2$ + 7$$, $$g(x) = x - 4$$, find $$(f - g)(3). $$

Accepted Answer

$$12$$

Question 5

Which of the following equations represents a circle with center $$(-8, 6)$$ and radius $$3$$?

Accepted Answer

$$(x + 8)^2$ + (y - 6)^2$ = 9$$

Question 6

Determine algebraically whether the function $$f(x) = x^2$ + x^3$ is even, odd, or neither.

Accepted Answer

Neither

Question 7

Find the distance between the points $$(7, 7)$$ and $$(-6, -7).$$

Accepted Answer

$$\sqrt{365}$$

Question 8

Which of the following best describes the symmetry of the graph of $$y = x^2$ - 4$$?

Accepted Answer

Symmetric with respect to the $$y-$$axis only

Question 9

Given $$f(x) = 16 - x^2$, g(x) = 4 - x$, find (f$$ \div g)(4)$$.

Accepted Answer

$$-4$$

Question 10

Which of the following lines is perpendicular to the line $$4x + y = 3$$ and passes through the point $$(2, 4)$$?

Accepted Answer

$$y = -\frac{1}{4}x + \frac{9}{2}$$

Question 11

Given the piecewise function $$f(x) = \begin{cases} 6 & 	ext{if } x \leq -1 \ 4 - 3x & 	ext{if } 0 \u003c x \u003c 3 \ x & 	ext{if } x \geq 3 \end{cases}$$, what is $$f(2)$$?

Accepted Answer

$$-2$$

Question 12

Which of the following statements about the function $$f(x) = x^3$ + 13x is $$true?

Accepted Answer

The function is odd.

Question 13

Given $$f(x) = \frac{2x}{x^2$ - 2}$$ and $$g(x) = \frac{2x + 3}{x}$$, are $$f$$ and $$g$$ inverses of each other?

Accepted Answer

No, because $$f(g(x)) 
eq x$$ for all $$x in $$the domain.

Question 14

A circle has the equation $$(x - 8)^2$ + (y - 6)^2$ = 9. $$What is the center and radius of the circle?

Accepted Answer

Center $$(8, 6)$$, radius $$3$$

Question 15

Which of the following equations is the slope-intercept form of the line passing through $$(9, 5)$$ and $$(0, -3)$$?

Accepted Answer

$$y = \frac{8}{9}x - 3$$

Question 16

Given $$f(x) = 5x^2$ + 5$$, what is $$f(-2)$$?

Accepted Answer

$$25$$

Question 17

Which of the following best describes the function $$f(x) = x^4$ + 2x + 8$$?

Accepted Answer

Neither even nor odd

Question 18

A real-world scenario: A company models its profit $$P(x) in $$thousands of dollars as $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units (in hundreds) produced. What is the maximum profit, and for how many units produced does it occur?

Accepted Answer

Maximum profit is $$18$$ thousand dollars at $$x = 2$$ hundred units.

Question 19

Which of the following is the correct equation of the line passing through $$(5, 2)$$ and parallel to the line $$2x + y = 4$$?

Accepted Answer

$$y = -2x + 12$$

Question 20

Suppose $$f(x) = x^2$ - 2x - 7$$ models the height (in meters) of a projectile at time $$x$$ seconds. At what time does the projectile reach its minimum height?

Accepted Answer

$$x = 1$$

College Algebra: Functions, Graphs, and Equations Study Guide

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