Question 1

Which of the following relations is NOT a function?

Accepted Answer

$$\{ (1, 2), (2, 3), (1, 4), (4, 5) \}$$

Question 2

Given the equation $$4x - x^2$ = y + 24$$, does this equation define $$y as a $$function of $$x$$?

Accepted Answer

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

Question 3

Find the value of the function $$f(x) = |x| + 2 at$$ $$x = -5.$$

Accepted Answer

$$7$$

Question 4

Given $$f(x) = 9x - 4$$ and $$g(x) = 2x + 6$$, find $$(f + g)(1).$$

Accepted Answer

$$21$$

Question 5

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

Accepted Answer

$$3$$

Question 6

Find the average rate of change of the function $$f(x) = 4x + 11$$ from $$x = 2 to$$ $$x = 5.$$

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 of $$f$$?

Accepted Answer

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

Question 9

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

Accepted Answer

Even

Question 10

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

Accepted Answer

The function is neither even nor odd, but $$f(x) \geq 0$$ for all $$x.$$

Question 11

A company charges a flat fee of \$$15 plus \2 $$per mile for a delivery. Write the cost $$C as a $$function of miles $$m$$, and find the cost for a 10-mile delivery.

Accepted Answer

$$C(m) = 2m + 15$$, $$C(10) = 35$$

Question 12

Given the graph of $$f(x) = -x^2$ + 8 (a $$downward opening parabola), what is the maximum value of $$f(x)$$ and at what $$x$$ does it occur?

Accepted Answer

Maximum at $$x = 0$$, $$f(0) = 8$$

Question 13

For the function $$f(x) = -2x^2$ + 8x + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 9)$$

Question 14

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

Accepted Answer

$$[-7, \infty)$$

Question 15

Given the function $$f(x) = x^2$ - 6x + 8$$, for which value of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 16

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t + 1. $$What is the maximum height reached by the ball?

Accepted Answer

$$21$$ meters

Question 17

Given the function $$f(x) = -x^2$ + 8.25$$, for which value of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = \pm 2.872$$

Question 18

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

Accepted Answer

$$x = 0$$

Question 19

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

Accepted Answer

It is symmetric with respect to the $$y-$$axis.

Question 20

Given the function $$f(x) = -x^2$ + 8.25$$, use the graph to determine the intervals where the function is increasing.

Accepted Answer

$$(-\infty, 0)$$

College Algebra: Functions, Graphs, and Their Properties

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