Question 1

Which of the following sets of ordered pairs represents a function?

Accepted Answer

$$\{(1, 4), (2, 5), (3, 6)\}$$

Question 2

A coffee shop models the cost to produce $$x$$ cups of coffee as $$C(x) = 2x + 50. $$What is the average rate of change in cost as production increases from $$10 to$$ $$20$$ cups?

Accepted Answer

$$2$$

Question 3

Given the function $$f(x) = |x|$$, which of the following best describes its domain and range in interval notation?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[0, \infty)$$

Question 4

A quadratic function $$f(x) = 2(x - 3)^2$ + 5 is $$transformed by reflecting it over the $$x-$$axis and shifting it up $$4$$ units. What is the new equation?

Accepted Answer

$$f(x) = -2(x - 3)^2$ + 9$$

Question 5

Which of the following graphs would fail the vertical line test?

Accepted Answer

A circle centered at $$(0,0)$$ with radius $$2$$

Question 6

Given $$f(x) = x^3$ - 4x^2$ + x - 6$$, use the Factor Theorem to determine which of the following is a zero of $$f(x).$$

Accepted Answer

$$x = 3$$

Question 7

A rocket's height is modeled by $$h(t) = -4.9t^2$ + 49t + 100. At $$what time does the rocket reach its maximum height?

Accepted Answer

$$t = 5$$ seconds

Question 8

What is the end behavior of the function $$f(x) = -3x^4$ + 2x^2$ - 7 as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 9

If $$g(x) = \frac{2x^2$ + 5x - 3}{x - 1}$$, what is the equation of the vertical asymptote?

Accepted Answer

$$x = 1$$

Question 10

A company’s average cost per unit is $$A(x) = \frac{8x + 200}{x}. $$What is the horizontal asymptote of $$A(x)$$, and what does it represent in context?

Accepted Answer

Horizontal asymptote: $$y = 8$$, representing the minimum average cost per unit as production increases.

Question 11

Given $$f(x) = x^2$ - 9$$ and $$g(x) = x + 3$$, what is $$(f \circ g)(2)$$?

Accepted Answer

$$0$$

Question 12

Which of the following rational functions has a hole at $$x = 2$$ and a vertical asymptote at $$x = -1$$?

Accepted Answer

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

Question 13

A polynomial $$p(x) = x^4$ - 2x^2$ + 3 is to be $$divided by $$x^2 - 1$. What placeholder term must be included in the dividend for correct long division setup?

Accepted Answer

$$0x^3$$

Question 14

Which of the following describes the end behavior of $$f(x) = -2x^5$ + 7x^3$ as x$$ 	o -\infty$$?

Accepted Answer

$$f(x) 	o \infty$$

Question 15

If $$f(x) = 3x^2$ + 6x + 8$$, what is the vertex form of $$f(x)$$?

Accepted Answer

$$f(x) = 3(x + 1)^2$ + 5$$

Question 16

A rational function $$r(x) = \frac{x^2$ - 4}{x^2$ - 1} is $$factored as $$\frac{(x-2)(x+2)}{(x-1)(x+1)}. $$What are the $$x-$$intercepts?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 17

A function $$f(x) = kx^p$$ has $$k \u003c 0$$ and $$p is $$even. What is the end behavior as $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 18

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

Accepted Answer

$$19$$

Question 19

A rational function $$f(x) = \frac{3x^2$ + 2x + 1}{x^2$ - 4} is $$given. What is the horizontal asymptote?

Accepted Answer

$$y = 3$$

MAT151 Precalculus: Core Concepts and Procedures for College Algebra

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