Q: Which of the following describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

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

Question 1

Given the graph of a cubic function with zeros at $$x = -2$$, $$x = 0$$, and $$x = 2$$, which of the following could be its equation?

Accepted Answer

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

Question 2

A polynomial function $$f(x)$$ has a graph that crosses the x-axis at $$x = 1$$ and touches the x-axis at $$x = -3. $$Which of the following could be the factored form of $$f(x)$$?

Accepted Answer

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

Question 3

Which of the following intervals represents the domain of the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

$$[2, \infty)$$

Question 4

Suppose the graph of $$y = f(x) is $$reflected over the x-axis and then shifted up by 3 units. What is the equation of the new graph?

Accepted Answer

$$y = -f(x) + 3$$

Question 5

Given the rational function $$f(x) = \frac{2x}{x-1}$$, what is the equation of its vertical asymptote?

Accepted Answer

$$x = 1$$

Question 6

Which of the following describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

Accepted Answer

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

Question 7

If $$f(x) = x^2$ - 4x + 3$$, what is the vertex of the parabola?

Accepted Answer

$$(2, -1)$$

Question 8

A company models its profit with $$P(x) = -x^2$ + 6x - 5$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$4 at$$ $$x = 3$$

Question 9

Which of the following is the solution set for $$|2x - 3| = 7$$?

Accepted Answer

$$\left\{ 5, -2 \right\}$$

Question 10

Which of the following graphs represents the function $$f(x) = \frac{1}{x}$$?

Accepted Answer

A graph with a vertical asymptote at $$x=0$$ and a horizontal asymptote at $$y=0$$, with branches in quadrants I and III.

Question 11

Solve the system of equations: $$\begin{cases} 2x + y = 5 \ x - y = 1 \end{cases}$$

Accepted Answer

$$(2, 1)$$

Question 12

Which of the following is the inverse of the function $$f(x) = 3x + 2$$?

Accepted Answer

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

Question 13

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

Accepted Answer

$$f(g(2)) = f(3) = 9$$

Question 14

Which of the following is the solution to the quadratic equation $$x^2 - 6x + 5 = 0$?

Accepted Answer

$$x = 1$$ and $$x = 5$$

Question 15

A real-world application: The height $$h (in $$meters) of a ball thrown upward from the ground is given by $$h(t) = -4.9t^2$ + 19.6t. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 2$$ seconds

Question 16

Which of the following intervals represents the range of the function $$f(x) = x^2$ - 4$$?

Accepted Answer

$$[-4, \infty)$$

Question 17

If $$f(x) = \sqrt{x+1}$$, for which value of $$x is$$ $$f(x)$$ defined?

Accepted Answer

$$x = -1$$

Question 18

Which of the following best describes the transformation from $$y = x^2$ to y$$ = $$(x-3)^2 + 2$?

Accepted Answer

Shift right 3 units and up 2 units

Question 19

Which of the following is the solution set for the inequality $$x^2 - 9$$ \u003c 0$$?

Accepted Answer

$$(-3, 3)$$

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