Question 1

Given the function $$f(x) = x^2$ + 8x - 9$$, what is the simplified form of the difference quotient $$\frac{f(x+h) - f(x)}{h}$$ for $$h 
eq 0$$?

Accepted Answer

$$2x + h + 8$$

Question 2

A chemical reaction's rate is modeled by $$f(x) = x^3$ - 3x^2$ + 1. $$According to the graph, at which points does the function have a relative maximum and minimum?

Accepted Answer

Maximum: $$(0, 1)$$; Minimum: $$(2, -3)$$

Question 3

For the functions $$f(x) = \frac{2}{x+4}$$ and $$g(x) = 5 - 6x$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$\frac{12x}{5 + 24x}$$

Question 4

A line passes through $$(5, 4)$$ and is perpendicular to the line $$y = 9x + 7. $$What is its equation in point-slope form?

Accepted Answer

$$y - 4 = -\frac{1}{9}(x - 5)$$

Question 5

Given $$f(x) = 8x^2$ - 8x$$ and $$g(x) = x^2$ - 2x - 7$$, what is the domain of $$\frac{f}{g}(x)$$?

Accepted Answer

Domain: $$(-\infty, 1 - \sqrt{2}) \cup (1 - \sqrt{2}, 1 + \sqrt{2}) \cup (1 + \sqrt{2}, \infty)$$

Question 6

Which of the following equations defines $$y as a $$function of $$x$$?

Accepted Answer

$$x + y^3$ = 64$$

Question 7

A medical researcher models the spread of a virus with $$f(x) = (x-4)^3$. What is the inverse function f$$^{-1}$$(x)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt[3]{x} + 4$$

Question 8

Given the relation $$\{(-3, 7), (-2, 2), (0, -2), (2, 2), (4, 14)\}$$, what are the domain and range?

Accepted Answer

Domain: $$\{-3, -2, 0, 2, 4\}$$; Range: $$\{7, 2, -2, 14\}$$

Question 9

A circle is given by $$(x-1)^2$$ + $$(y+2)^2 = 36$. What is its center and radius?

Accepted Answer

Center: $$(1, -2)$$, $$r = 6$$

Question 10

A business tracks the percent of students in engineering from 1950 to 2000. Does the graph represent a function?

Accepted Answer

Yes

Question 11

Given $$f(x) = 3x + 1$$ and $$g(x) = \sqrt{x + 4}$$, what is the domain of $$f + g$$?

Accepted Answer

$$[-4, \infty)$$

Question 12

A line passes through $$(-7, 6)$$ with slope $$-3. $$What is its equation in slope-intercept form?

Accepted Answer

$$y = -3x - 15$$

Question 13

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

Accepted Answer

$$1,093$$

Question 14

Which of the following functions is even?

Accepted Answer

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

Question 15

A function $$f(x) is $$graphed and passes the vertical line test. Does it have an inverse function?

Accepted Answer

Yes

Question 16

Given $$f(x) = 4x + 4$$ and $$g(x) = \sqrt{x}$$, what is the domain of $$f \circ g$$?

Accepted Answer

$$[0, \infty)$$

Question 17

A researcher wants to model a population with $$f(x) = 3. $$What is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$ for $$h 
eq 0$$?

Accepted Answer

$$0$$

Question 18

Given the equation $$y + 8 = 0$$, what is the slope and $$y-$$intercept of the line?

Accepted Answer

$$m = 0; (0, -8)$$

College Algebra Unit 2 Review – Step-by-Step Study Guidance

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드