Question 1

Given the relation $$\{(6, -5), (3, 2), (4, 6), (-1, 3), (-4, 9)\}$$, what is the domain and range of the relation?

Accepted Answer

Domain: $$\{6, 3, 4, -1, -4\}$$; Range: $$\{-5, 2, 6, 3, 9\}$$

Question 2

Determine whether the relation $$\{(-3, -6), (2, -6), (5, -5), (7, 9), (11, -5)\} is a $$function.

Accepted Answer

Yes, because each $$x-$$value is paired with exactly one $$y-$$value.

Question 3

Does the equation $$x^2$$ + $$y^2 = 36$ define y$ as a function of x$?

Accepted Answer

No, because for some $$x$$ there are two possible $$y$$ values.

Question 4

Evaluate $$f(x-1)$$ for $$f(x) = 2x^2$ + 2x - 2$$ and simplify.

Accepted Answer

$$2x^2 - 2x - 2$

Question 5

A vendor's profit is modeled by $$P(x) = 0.7x - 66. $$What is the profit from selling 800 pretzels?

Accepted Answer

$$494$$

Question 6

Given the graph in image 1, what is $$f(-4)$$?

Accepted Answer

$$12$$

Question 7

Given the graph in image 2, what is the domain and range of the function?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, 5]$$

Question 8

For the function graphed in image 3, on which interval is the function increasing?

Accepted Answer

$$(-2, -1)$$

Question 9

Determine whether $$f(x) = 5x^2$ + x^4$ is even, odd, or neither.

Accepted Answer

Even

Question 10

Evaluate the piecewise function $$g(x) = \begin{cases} \frac{x^2$ - 5}{x - 8} & x 
eq 8 \ x - 7 & x = 8 \end{cases} at$$ $$x = 5.$$

Accepted Answer

$$-\frac{20}{3}$$

Question 11

Find and simplify the difference quotient $$\frac{f(x+h) - f(x)}{h}$$ for $$f(x) = 4x - 5$$, $$h 
eq 0.$$

Accepted Answer

$$4$$

Question 12

Find the slope of the line passing through $$(5, 8)$$ and $$(-2, 8).$$

Accepted Answer

$$0$$

Question 13

Write the equation of the line in slope-intercept form passing through $$(4, 4)$$ and $$(5, 7). $$

Accepted Answer

$$y = 3x - 8$$

Question 14

Write the equation of the line passing through $$(4, 5)$$ and perpendicular to $$y = 4x + 7 in $$point-slope form.

Accepted Answer

$$y - 5 = -\frac{1}{4}(x - 4)$$

Question 15

Find the average rate of change of $$f(x) = -3x^2$ - x$$ from $$x_1 = 5$ to x_2$ = 6.$$

Accepted Answer

$$-34$$

Question 16

Given $$f(x) = 7x^2$ - 9x$$ and $$g(x) = x^2$ - 5x - 36$$, find $$\frac{f(x)}{g(x)}.$$

Accepted Answer

$$\frac{7x^2$ - 9x}{x^2$ - 5x - 36}$$

Question 17

A company has cost $$C(x) = 75x + 7410$$ and revenue $$R(x) = 85x$$ for up to 831 units. What is $$(R - C)(831)$$ and what does it represent?

Accepted Answer

$$900$$, profit; income exceeds cost

Question 18

Given $$f(x) = -6x + 5$$ and $$g(x) = 4x + 7$$, find $$(g \circ f)(x).$$

Accepted Answer

$$-24x + 27$$

Question 19

Which two functions are inverses of each other? Assume $$x \u003e 0$$.

$$f(x) = \frac{x + 3}{4}$$
$$g(x) = 4x + 3$$
$$h(x) = 4x - 3$$

Accepted Answer

$$g(x)$$ and $$h(x)$$

Question 20

Find the inverse of $$f(x) = (x - 8)^3$.

Accepted Answer

$$f^{-1}(x$$) = \sqrt[3]{x} + 8$$

College Algebra Unit 2 Study Guide: Functions, Graphs, and Equations

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