As $$x \to \infty$$, $$p(x) \to -\infty$$; as $$x \to -\infty$$, $$p(x) \to \infty$$

Question 1

Which of the following statements correctly describes the Vertical Line Test for functions?

Accepted Answer

A graph represents a function if and only if every vertical line intersects the graph at most once.

Question 2

Given the function $$f(x) = x^3$ + 3x + 2$$ and $$g(x) = x^4$ - 4$$, what is the domain of $$f - g$$?

Accepted Answer

All real numbers

Question 3

Suppose $$f(x) = \dfrac{4}{x^2$}$$ and $$g(x) = x^2$. What is the domain of f$$ \circ g$$?

Accepted Answer

$$x 
eq 0$$

Question 4

Which transformation results in a horizontal shift of the graph of $$f(x) to $$the left by 2 units?

Accepted Answer

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

Question 5

Given $$f(x) = 2x - 1$$ and $$g(x) = \dfrac{x+1}{2}$$, which of the following is true?

Accepted Answer

$$f$$ and $$g$$ are inverse functions of each other.

Question 6

For the function $$f(x) = x^2$ + 1$$, which of the following statements is true?

Accepted Answer

$$f(x) is $$not one-to-one and does not have an inverse over all real numbers.

Question 7

A rancher has 600 yards of fencing to enclose a rectangular corral with a partition as shown. What are the dimensions that maximize the area?

Accepted Answer

$$x = 100$$ yards, $$y = 200$$ yards

Question 8

Given $$f(x) = \dfrac{x^2$ - 4x + 5}{2x}$$, which of the following is a vertical asymptote?

Accepted Answer

$$x = 0$$

Question 9

Which of the following is the correct inverse of $$f(x) = x^3$ + 1$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt[3]{x - 1}$$

Question 10

Let $$P(x) = 2x^3$ - 13x^2$ + 11x + 25. If$$ $$x = 5 is a $$zero, what are the remaining zeros?

Accepted Answer

$$x = -1, x = 2.5$$

Question 11

Which of the following best describes the end behavior of $$p(x) = -x^3$ + 6x^2$ - 9x$$?

Accepted Answer

As $$x 	o \infty$$, $$p(x) 	o -\infty$$; as $$x 	o -\infty$$, $$p(x) 	o \infty$$

Question 12

Which of the following is a possible rational zero of $$f(x) = 4x^5$ + 18x^4$ - 6x^3$ - 7x^2$ + x - 6$$ according to the Rational Root Theorem?

Accepted Answer

$$\pm1$$

Question 13

Given the piecewise function $$h(x) = \begin{cases} x^2$, & x \leq 2 \ 6 - x, & x \u003e 2 \end{cases}$$, on which interval is $$h(x)$$ decreasing?

Accepted Answer

$$(2, \infty)$$

Question 14

Which of the following is the vertex of the parabola $$f(x) = \dfrac{1}{2}(x - 1)^2$ - 3$$?

Accepted Answer

$$(1, -3)$$

Question 15

If $$f(x) is a $$function and passes the Horizontal Line Test, which of the following is true?

Accepted Answer

$$f(x) is $$one-to-one and has an inverse function.

Question 16

Which of the following describes the transformation from $$f(x) to$$ $$f(-x)$$?

Accepted Answer

Reflection across the $$y-$$axis

Question 17

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

Accepted Answer

$$(f \circ g)(x) = (x + 1)^2$

Question 18

Which of the following is the correct equation for a line passing through $$(2, 3)$$ with slope $$-4$$?

Accepted Answer

$$y - 3 = -4(x - 2)$$

Question 19

Which of the following is the correct parent function for $$h(x) = 2\sqrt{x + 1} - 3$$?

Accepted Answer

$$f(x) = \sqrt{x}$$

College Algebra Practice Test 2: Functions, Graphs, Transformations, and Polynomial Analysis

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