Q: Which of the following best describes the end behavior of the function $$f(x) = -3x^4$ + 2x^2$ - 7$$?

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

Question 1

Which of the following is the correct solution to the equation $$\sqrt{x+5} = 3$$?

Accepted Answer

$$x = 4$$

Question 2

A biologist is studying the growth of a bacterial colony, which can be modeled by the function $$N(t) = 200 \cdot 2^t$$, where $$N is $$the number of bacteria and $$t is $$the time in hours. How many bacteria will there be after 3 hours?

Accepted Answer

$$1600$$

Question 3

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 4

Given the function $$f(x) = 2x^2$ - 4x + 1$$, which of the following describes the effect of replacing $$x$$ with $$x-3 in $$the function?

Accepted Answer

The graph shifts 3 units to the right.

Question 5

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 12x - 16$$, 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 $$20$$ thousand dollars at $$x = 3$$ thousand units.

Question 6

Which of the following is the correct solution set for the inequality $$2x - 5 \u003c 7$$?

Accepted Answer

$$x \u003c 6$$

Question 7

If $$f(x) = 3x - 2$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$10$$

Question 8

Which of the following best describes the domain of the function $$f(x) = \dfrac{1}{x-4}$$?

Accepted Answer

All real numbers except $$x = 4$$

Question 9

A line passes through the points $$(1, 2)$$ and $$(3, 6). $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = 2x$$

Question 10

Which transformation is applied to the graph of $$y = f(x) to $$obtain $$y = f(-x)$$?

Accepted Answer

Reflection across the $$y-$$axis

Question 11

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

Accepted Answer

$$[0, \infty)$$

Question 12

A chemical reaction’s temperature $$T (in $$degrees Celsius) over time $$t (in $$minutes) is modeled by $$T(t) = 5t + 20. $$What is the temperature after 8 minutes?

Accepted Answer

$$60$$ degrees Celsius

Question 13

Which of the following is the correct vertex form of the quadratic $$y = x^2$ - 6x + 5$$?

Accepted Answer

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

Question 14

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

Accepted Answer

$$x^2 + 2x + 1$

Question 15

A medical researcher models the concentration $$C of a $$drug in the bloodstream by $$C(t) = 50e$$^{-0.2t}$$, where t$ is in hours. What is the concentration after 5 hours? (Round to the nearest whole number.)

Accepted Answer

$$18$$

Question 16

Which of the following is the solution to the system of equations: $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(2, 3)$$

Question 17

Which of the following best describes the end behavior of the function $$f(x) = -3x^4$ + 2x^2$ - 7$$?

Accepted Answer

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

Question 18

If the line $$y = 2x + 1 is $$perpendicular to another line, what is the slope of the other line?

Accepted Answer

$$-\dfrac{1}{2}$$

Question 19

Which of the following is the correct solution to the equation $$|3x - 4| = 8$$?

Accepted Answer

$$x = 4 or$$ $$x = -\dfrac{4}{3}$$

Question 20

A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 19.6t + 2. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$2$$ seconds

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