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

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

Accepted Answer

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

Question 2

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

Accepted Answer

$$-4$$

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

Which of the following graphs is NOT the graph of a function?

Accepted Answer

A graph that fails the vertical line test.

Question 5

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 6

If $$f(x) = x + 5$$ and $$g(x) = x - 4$$, what is $$(f - g)(x)$$?

Accepted Answer

$$9$$

Question 7

Given $$f(x) = 5x^2$ - 5$$ and $$g(x) = 3x^2$ - 5x - 4$$, what is $$(f + g)(x)$$?

Accepted Answer

$$8x^2 - 5x - 9$

Question 8

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

Accepted Answer

Neither

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

$$\sqrt{365}$$

Question 11

What is the equation of the circle with center $$(-8, 6)$$ and radius $$3$$?

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Given the line passing through $$(3, 5)$$ with slope $$m = -3$$, what is its equation in point-slope form?

Accepted Answer

$$y - 5 = -3(x - 3)$$

Question 14

Which of the following statements about the function $$f(x) = x^4$ + 2x + 8 is $$true?

Accepted Answer

It is neither even nor odd.

Question 15

A hospital monitors the temperature of a patient every hour. The temperature $$T in $$degrees Celsius is modeled by $$T(t) = -0.5t^2$ + 2t + 37$$, where $$t is $$the number of hours after admission. What is the maximum temperature and at what time does it occur?

Accepted Answer

Maximum temperature is $$39$$°C at $$t = 2$$ hours.

Question 16

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

Accepted Answer

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

Question 17

Given $$f(x) = 16 - x^2$ and g(x) = 4 - x$, what is (f$$ \div g)(x)$$?

Accepted Answer

$$\frac{16 - x^2$}{4 - x}$$

Question 18

A circle has the equation $$(x - 8)^2$ + (y - 8)^2$ = 64. $$What is the center and radius of the circle?

Accepted Answer

Center $$(8, 8)$$, radius $$8$$

Question 19

Which of the following best describes the transformation to obtain the graph of $$f(x) = x^2$ - 2x - 7$$ from $$y = x^2$?

Accepted Answer

Shift 1 unit right and 7 units down.

College Algebra: Functions, Graphs, and Equations Study Guide

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