Question 1

Given the function $$f(x) = \begin{cases} 2x + 1 & 	ext{if } x \u003c 0 \ x^2$ & 	ext{if } x \geq 0 \end{cases}$$, what is the value of $$f(-3)$$?

Accepted Answer

$$7$$

Question 2

A company’s profit $$P(x) in $$thousands of dollars is given by $$P(x) = -2x^2$ + 8x + 5$$, 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 $$13$$ thousand dollars at $$x = 2$$ thousand units.

Question 3

Given $$f(x) = x^2$ - 4x + 3$$ and $$g(x) = 2x - 1$$, find $$(f + g)(2).$$

Accepted Answer

$$6$$

Question 4

If $$h(x) = \sqrt{9 - x^2$}$$, what is the domain of $$h(x) in $$interval notation?

Accepted Answer

$$[-3, 3]$$

Question 5

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

Accepted Answer

$$10$$

Question 6

A piecewise function is defined as $$f(x) = \begin{cases} x + 2 & 	ext{if } x \u003c 1 \ 2x - 1 & 	ext{if } x \geq 1 \end{cases}. $$What is $$f(1)$$?

Accepted Answer

$$1$$

Question 7

Given the function $$f(x) = x^3$ - 6x^2$ + 9x$$, find the intervals where the function is increasing.

Accepted Answer

$$(-\infty, 1) \cup (3, \infty)$$

Question 8

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

Accepted Answer

$$9$$

Question 9

A function $$f(x) is $$defined for $$x \in [0, 5]. $$What is the average rate of change of $$f(x) = 2x + 3$$ from $$x = 1 to$$ $$x = 4$$?

Accepted Answer

$$2$$

Question 10

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

Accepted Answer

$$8$$

Question 11

A medication’s concentration in the bloodstream is modeled by $$C(t) = 5e$$^{-0.2t}$$, where t$ is time in hours. What is the domain of C(t$$)$$?

Accepted Answer

$$[0, \infty)$$

Question 12

Given $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, find $$(f \circ g)(3).$$

Accepted Answer

$$21$$

Question 13

If $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f(x) in $$interval notation?

Accepted Answer

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

Question 14

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

Accepted Answer

$$5$$

Question 15

A piecewise function is defined as $$f(x) = \begin{cases} x^2$ & 	ext{if } x \u003c 2 \ 3x - 4 & 	ext{if } x \geq 2 \end{cases}. $$What is $$f(3)$$?

Accepted Answer

$$5$$

Question 16

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

Accepted Answer

$$-2$$

Question 17

A population of bacteria is modeled by $$P(t) = 1000e$$^{0.05t}$$, where t$ is time in hours. What is the average rate of change of the population from t = 0$ to t = 10$?

Accepted Answer

$$1000(e^{0.5} - 1) / 10$

Question 18

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

Accepted Answer

$$8$$

Question 19

If $$f(x) = \frac{1}{x}$$ and $$g(x) = x - 2$$, what is $$(f \circ g)(4)$$?

Accepted Answer

$$\frac{1}{2}$$

Question 20

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

Accepted Answer

$$36$$

Functions: Evaluation, Domain, Range, and Composition in College Algebra

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