Q: Which of the following describes the end behavior of $$f(x) = -2x^4$ + 5x^2$ - 1$$?

As $$x \to \pm\infty$$, $$f(x) \to -\infty$$

Question 1

Which of the following graphs represents a function according to the Vertical Line Test?

Accepted Answer

A graph where every vertical line intersects the curve at most once.

Question 2

Given the function $$f(x) = |x-3| + 2$$, what is the range of $$f(x)$$?

Accepted Answer

$$[2, \infty)$$

Question 3

Which of the following is the correct interval notation for the domain of $$f(x) = \sqrt{x-5}$$?

Accepted Answer

$$[5, \infty)$$

Question 4

A function $$f is $$defined as $$f(x) = \frac{1}{x-2}. $$Which of the following statements is true?

Accepted Answer

The function has a vertical asymptote at $$x=2.$$

Question 5

If $$f(x) = 2x^2$ - 4x + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(1, -1)$$

Question 6

Which of the following functions is one-to-one?

Accepted Answer

$$f(x) = x^3$

Question 7

A company models its profit with $$P(x) = -3x^2$ + 12x - 5$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and at how many units sold does it occur?

Accepted Answer

Maximum profit is $$13 at$$ $$x=2$$ thousand units.

Question 8

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

Accepted Answer

$$9$$

Question 9

Which of the following describes the end behavior of $$f(x) = -2x^4$ + 5x^2$ - 1$$?

Accepted Answer

As $$x 	o \pm\infty$$, $$f(x) 	o -\infty$$

Question 10

Which of the following is the inverse of $$f(x) = 3x - 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x+7}{3}$$

Question 11

A rational function $$f(x) = \frac{x^2$ - 9}{x^2$ - 4}$$ has which of the following features?

Accepted Answer

Vertical asymptotes at $$x=2$$ and $$x=-2$$; removable discontinuity at none.

Question 12

Which transformation describes the graph of $$f(x) = -|x-4| + 2$$ compared to $$f(x) = |x|$$?

Accepted Answer

Shift right 4 units, reflect over $$x-$$axis, shift up 2 units

Question 13

If $$f(x) = x^2$ - 4$$ and $$g(x) = x-2$$, what is $$\frac{f(x)}{g(x)}$$ and what type of discontinuity does it have?

Accepted Answer

$$\frac{f(x)}{g(x)} = x+2$$ with a removable discontinuity at $$x=2$$

Question 14

A piecewise function is defined as $$f(x) = \begin{cases} x+2 & x \u003c 0 \ x^2$ & x \geq 0 \end{cases}. $$What is $$f(-3) + f(2)$$?

Accepted Answer

$$7$$

Question 15

Which of the following best describes the range of $$f(x) = \frac{1}{x}$$?

Accepted Answer

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

Question 16

A medical researcher models the concentration of a drug in the bloodstream over time as $$C(t) = 5e$$^{-0.2t}$$, where t$ is in hours. What is the domain and range of C(t$$)$$?

Accepted Answer

Domain: $$[0, \infty)$$; Range: $$(0, 5]$$

Question 17

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

Accepted Answer

$$16$$

Question 18

Which of the following statements about the function $$f(x) = \sqrt{x} is $$true?

Accepted Answer

The domain is $$[0, \infty)$$ and the range is $$[0, \infty).$$

Question 19

A polynomial $$p(x) is $$divided by $$(x-3)$$ using synthetic division and the remainder is $$5. $$What does this tell you about $$p(3)$$?

Accepted Answer

$$p(3) = 5$$

College Algebra: Functions and Polynomial Fundamentals

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