Question 1

Which of the following relations is NOT a function?

Accepted Answer

$$\{ (1, 4), (3, 10), (0, 1), (3, 11), (5, 23) \}$$

Question 2

Does the equation $$4x - x^2$ = y + 24$$ define $$y as a $$function of $$x$$?

Accepted Answer

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

Question 3

Given $$f(x) = |x| + 2$$, what is $$f(-5) - f(5)$$?

Accepted Answer

$$0$$

Question 4

Given $$f(x) = x^2$ + 3x - 1$$, what is $$f(0)$$?

Accepted Answer

$$-1$$

Question 5

Given $$f(x) = x^2$ + 3x - 1$$ and $$g(x) = 2x + 6$$, find $$(f + g)(1).$$

Accepted Answer

$$12$$

Question 6

Find the average rate of change of the function $$f(x) = 4x + 11$$ from $$x = 2 to$$ $$x = 6.$$

Accepted Answer

$$4$$

Question 7

Find the slope of the line passing through the points $$(-2, 4)$$ and $$(1, 9).$$

Accepted Answer

$$\dfrac{5}{3}$$

Question 8

Given the graph of $$f(x) = x^2$ - 4 (a $$parabola opening upwards), what is the domain and range?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[-4, \infty)$$

Question 9

Given $$f(x) = |x|$$, determine if the function is even, odd, or neither.

Accepted Answer

Even

Question 10

Suppose a company models its profit with $$P(x) = -2x^2$ + 8x + 5$$, 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 $$21 at$$ $$x = 2$$ thousand units.

Question 11

Given the function $$f(x) = |x| - |x - 1|$$, what is $$f(2)$$?

Accepted Answer

$$0$$

Question 12

Given the function $$f(x) = |x|$$, which of the following statements is true?

Accepted Answer

$$f(-x) = f(x)$$ for all $$x$$

Question 13

Given the graph of $$f(x) = -x^2$ + 8 (as in $$Figure 2), for which value of $$x$$ does $$f(x) = 8.25$$?

Accepted Answer

$$x = 0.5$$

Question 14

For the function $$f(x) = -x^2$ + 8$$, as shown in Figure 2, on which interval is the function increasing?

Accepted Answer

$$(-\infty, 0)$$

Question 15

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 14t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$12$$ meters

Question 16

Given $$f(x) = |x| - 7$$, what is the range of $$f$$?

Accepted Answer

$$[-7, \infty)$$

Question 17

Given $$f(x) = x^2$ - 4x + 3$$, for which value(s) of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 18

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

Accepted Answer

$$25$$

Question 19

A medical researcher models the spread of a virus with $$N(t) = 1000e$$^{0.2t}$$, where N$ is the number of cases and t$ is days since the outbreak. How many cases are there after 5 days? (Round to the nearest whole number.)

Accepted Answer

$$2718$$

Question 20

Given $$f(x) = |x|$$, which of the following best describes the symmetry of its graph?

Accepted Answer

Symmetric with respect to the $$y-$$axis

College Algebra: Functions, Graphs, and Their Properties

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