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

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

Question 1

Which of the following best describes the definition of a function?

Accepted Answer

A relation where each input is paired with exactly one output.

Question 2

Given the function $$f(x) = 2x^2$ - 3x + 1$$, which of the following is the correct result for $$f(-2)$$?

Accepted Answer

$$f(-2) = 15$$

Question 3

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

Accepted Answer

$$(g \circ h)(2) = 9$$

Question 4

Which transformation will reflect the graph of $$f(x)$$ over the $$x-$$axis?

Accepted Answer

$$y = -f(x)$$

Question 5

A company models its profit with the quadratic function $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$26 at$$ $$x = 2$$ thousand units.

Question 6

Which of the following is the correct factorization of $$x^3$$ - $$6x^2 + 11x - 6$?

Accepted Answer

$$(x - 1)(x - 2)(x - 3)$$

Question 7

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

Accepted Answer

$$(f + g)(x) = x^2$ + x - 2$$

Question 8

Which of the following is the inverse of the function $$f(x) = 3x - 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 5}{3}$$

Question 9

A radioactive substance decays according to $$A(t) = 100e$$^{-0.05t}$$, where A$ is the amount remaining after t$ years. How much remains after 20$ years (rounded to the nearest whole number)?

Accepted Answer

$$37$$

Question 10

Solve for $$x$$: $$2^{x} = 16$.

Accepted Answer

$$x = 4$$

Question 11

Which of the following is equivalent to $$\log_{2} 32$$?

Accepted Answer

$$5$$

Question 12

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$x \geq 0$$

Question 13

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

Accepted Answer

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

Question 14

Solve the inequality $$\frac{x - 2}{x + 1} \u003e 0.$$

Accepted Answer

$$x \u003e 2 or$$ $$x \u003c -1$$

Question 15

Which of the following is the equation of a circle with center at $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 25$$

Question 16

Solve the system of equations: $$\begin{cases} x + y + z = 6 \ x - y + z = 2 \ x + y - z = 0 \end{cases}$$

Accepted Answer

$$x = 2, y = 2, z = 2$$

Question 17

Which of the following is the expanded form of $$(x + 2)^4$ using the Binomial Theorem?

Accepted Answer

$$x^4$$ + $$8x^3$$ + $$24x^2 + 32x + 16$

Question 18

A population of bacteria triples every 5 hours. If the initial population is 200, what will the population be after 10 hours?

Accepted Answer

$$1800$$

Question 19

Which of the following is the solution set for the system of inequalities $$y \u003e x^2$ and y$$ \u003c 4$$?

Accepted Answer

The region above $$y = x^2$ and below y = 4$

Precalculus Course Outline and Topic Overview (Math 112)

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