Question 1

Given the equation of a line $$2x - 3y = 6$$, what is the equation of a line perpendicular to it that passes through the point $$(1, -2)$$? Leave your answer in general form.

Accepted Answer

$$3x + 2y = -1$$

Question 2

Find the equation of the line that passes through the points $$(2, 5)$$ and $$(4, 9). $$Express your answer in slope-intercept form.

Accepted Answer

$$y = 2x + 1$$

Question 3

If the average rate of change of a function $$f(x)$$ from $$x = 1 to$$ $$x = 4 is$$ $$5$$, which of the following could be the value of $$f(4) if$$ $$f(1) = 2$$?

Accepted Answer

$$f(4) = 17$$

Question 4

A graph of $$y = f(x) is $$provided. If you apply the transformation $$g(x) = f(x-2) + 3$$, what happens to the graph?

Accepted Answer

It shifts right by 2 units and up by 3 units.

Question 5

Find the domain of the function $$f(x) = \dfrac{1}{x^2$ - 9}.$$

Accepted Answer

$$(-\infty, -3) \cup (-3, 3) \cup (3, \infty)$$

Question 6

Which of the following is the parent function for a quadratic equation?

Accepted Answer

$$f(x) = x^2$

Question 7

Given $$f(x) = 2x + 1$$ and $$g(x) = x^2$, find (f + g)(3$$)$$.

Accepted Answer

$$16$$

Question 8

If $$f(x) = x^3$ and g(x) = x + 2$, what is (f$$ \circ g)(1)$$?

Accepted Answer

$$27$$

Question 9

Which of the following functions has an inverse that is also a function?

Accepted Answer

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

Question 10

Given $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, which pair of functions are inverses of each other for x$$ \geq 0$$?

Accepted Answer

$$f(x)$$ and $$g(x)$$

Question 11

Given the equation $$y = 5x - 7$$, what is the equation for its inverse?

Accepted Answer

$$y = \dfrac{x + 7}{5}$$

Question 12

If $$f(x) = 2x - 3$$, find $$f^{-1}(x$$)$$.

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x + 3}{2}$$

Question 13

Given $$f(x) = x^2$ and g(x) = x + 1$, find (f$$ \circ g)(2)$$.

Accepted Answer

$$9$$

Question 14

Which of the following is the correct difference quotient for $$f(x) = x^2$?

Accepted Answer

$$\dfrac{(x+h)^2$ - x^2$}{h}$$

Question 15

A medical researcher models the growth of bacteria with $$N(t) = 100e$$^{0.5t}$$. What is the population after 4 hours?

Accepted Answer

$$N(4) = 100e$$^{2}$$

Question 16

A chemical reaction rate is modeled by $$R(t) = 5t^2$ - 3t + 2. $$What is the average rate of change from $$t = 1 to$$ $$t = 3$$?

Accepted Answer

$$16$$

Question 17

Which of the following is NOT a function?

Accepted Answer

$$y^2 = x$

Question 18

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

Accepted Answer

$$16$$

Question 19

A company’s profit $$P(x) is $$modeled by $$P(x) = -2x^2$ + 40x - 100$$, where $$x is $$the number of units sold. What is the maximum profit?

Accepted Answer

$$P(10) = 100$$

College Algebra: Study Guide on Functions, Transformations, and Operations

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