Q: Which of the following best describes the end behavior of $$f(x) = -2x^4$ + 3x^2$ - 1$$?

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

Q: Which of the following describes the end behavior of $$f(x) = x^5$ - 2x^3$ + x$$?

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

Question 1

Which of the following describes the sequence of transformations needed to graph $$h(x) = (x-2)^2$ - 3$$ using the parent function $$f(x) = x^2$?

Accepted Answer

Shift the graph of $$f(x)$$ right 2 units and down 3 units.

Question 2

Given $$f(x) = \sqrt{x+1}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$[-1, \infty)$$

Question 3

Suppose $$g(x) = \dfrac{2x+1}{x-3}. $$Which of the following statements is true about the graph of $$g(x)$$?

Accepted Answer

There is a vertical asymptote at $$x = 3$$ and a horizontal asymptote at $$y = 2$$

Question 4

A ball is thrown upward from a height of 8 feet. Its height after $$x$$ feet of horizontal distance is given by $$h(x) = -0.02x^2$ + 0.5x + 8. $$What is the maximum height the ball reaches?

Accepted Answer

$$9.25$$ feet

Question 5

Given $$f(x) = x^3$ - 4x$$, determine whether the function has a maximum or minimum value and state the value.

Accepted Answer

The function has neither a maximum nor a minimum value.

Question 6

Find the zeros of the polynomial $$f(x) = x^3$ - 4x^2$ + 4x.$$

Accepted Answer

$$x = 0, 2, 2$$

Question 7

Which of the following rational functions has a hole at $$x = 2$$?

Accepted Answer

$$f(x) = \dfrac{x-2}{x^2$-4}$$

Question 8

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

Accepted Answer

$$9$$

Question 9

Which of the following best describes the end behavior of $$f(x) = -2x^4$ + 3x^2$ - 1$$?

Accepted Answer

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

Question 10

Given $$f(x) = \sqrt{x-1}$$, which of the following intervals represents the domain of $$f(x)$$?

Accepted Answer

$$[1, \infty)$$

Question 11

Which of the following is the inverse of $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x-5}{2}$$

Question 12

A company’s profit per day by selling $$x$$ products is given by $$P(x) = -0.01x^2$ + 3.22x + 400. $$How many products should be sold to maximize profit?

Accepted Answer

$$161$$

Question 13

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

Accepted Answer

$$-2$$

Question 14

Which of the following is NOT a polynomial function?

Accepted Answer

$$f(x) = \dfrac{1}{x}$$

Question 15

Find the horizontal asymptote of $$f(x) = \dfrac{3x^2$ + 1}{x^2$ - 4}.$$

Accepted Answer

$$y = 3$$

Question 16

Given $$f(x) = x^2$ - 4x + 3$$, which of the following statements about its zeros is correct?

Accepted Answer

The zeros are $$x = 1$$ and $$x = 3.$$

Question 17

Which of the following best describes the symmetry of the function $$f(x) = x^4$?

Accepted Answer

Even symmetry (about the $$y-$$axis)

Question 18

Given $$f(x) = \dfrac{1}{x^2$}$$, which of the following is true about its domain?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 19

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

Accepted Answer

$$(2x + 1)^2$

Question 20

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

Accepted Answer

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

College Algebra Study Guide: Functions, Graphs, Transformations, and Polynomial/Rational Analysis

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