Question 1

Evaluate $$(fg)(-2)$$ for $$f(x) = x + 1$$ and $$g(x) = 2x^2$ + 15x + 6. $$What is the value?

Accepted Answer

$$16$$

Question 2

Complete the square for $$x^2 - 6x + 9$$ + $$y^2 + 6y + 9 = 36$ and write the equation in standard form. What are the center and radius of the circle?

Accepted Answer

$$(x - 3)^2$ + (y + 3)^2$ = 36$$; Center: $$(3, -3)$$, Radius: $$6$$

Question 3

For $$f(x) = -5x + 9$$ and $$g(x) = 2x + 3$$, find $$(g \circ f)(x).$$

Accepted Answer

$$-10x + 21$$

Question 4

Given $$f(x) = \frac{x - 5}{7}$$ and $$g(x) = 7x + 5$$, what is $$(g \circ f)(x)$$?

Accepted Answer

$$x$$

Question 5

Find $$(g \circ f)(20)$$ for $$f(x) = \frac{x - 2}{6}$$ and $$g(x) = 4x + 9.$$

Accepted Answer

$$21$$

Question 6

Which two functions are inverses of each other? $$f(x) = 9x$$, $$g(x) = \frac{x}{9}$$, $$h(x) = \frac{9}{x}$$

Accepted Answer

f(x) and g(x)

Question 7

Find the midpoint of the line segment with endpoints $$\left(-\frac{8}{3}, -\frac{7}{5}\right)$$ and $$\left(\frac{7}{3}, -\frac{9}{5}\right).$$

Accepted Answer

$$\left(-\frac{1}{6}, -\frac{8}{5}\right)$$

Question 8

Write the standard form of the equation of the circle with center $$(-5, -4)$$ and radius $$19.$$

Accepted Answer

$$(x + 5)^2$ + (y + 4)^2$ = 19$$

Question 9

Find the domain of the composite function $$f \circ g$$ where $$f(x) = \frac{4}{x + 7}$$ and $$g(x) = x + 3.$$

Accepted Answer

$$(-\infty, -10) \cup (-10, \infty)$$

Question 10

Find the inverse of the function $$f(x) = \frac{3x - 4}{5}.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{5x + 4}{3}$$

Question 11

Describe how the graph of $$f(x) = (x - 2)^2$ + 4$$ relates to the graph of $$y = x^2$.

Accepted Answer

A translation 2 units to the right and 4 units up

Question 12

Find the domain of $$h(x) = \frac{x - 2}{x^3$ - 4x}.$$

Accepted Answer

$$(-\infty, -2) \cup (-2, 0) \cup (0, 2) \cup (2, \infty)$$

Question 13

Given $$f(x) = 2 - 5x$$ and $$g(x) = -7x^2$ + 5$$, find $$(f + g)(x).$$

Accepted Answer

$$-7x^2 - 5x + 7$

Question 14

Find the distance between the points $$(-\frac{4}{7}, -2)$$ and $$(-\frac{3}{7}, 1).$$

Accepted Answer

$$4$$

Question 15

Find the average rate of change of $$f(x) = 5x + 7$$ from $$x_1 = -1$ to x_2$ = 0.$$

Accepted Answer

$$5$$

Question 16

Write the equation of the line passing through $$(3, 5)$$ and perpendicular to $$-4x + y - 6 = 0 in $$slope-intercept form.

Accepted Answer

$$y = -\frac{1}{4}x + \frac{23}{4}$$

Question 17

Find the slope of the line passing through $$(-3, 3)$$ and $$(-2, 3).$$

Accepted Answer

$$0$$

Question 18

Find the average rate of change of $$f(x) = 2x$$ from $$x_1 = 2$ to x_2$ = 8.$$

Accepted Answer

$$\frac{1}{3}$$

College Algebra Test #2 Review – Step-by-Step Guidance

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