Question 1

Which of the following expressions is equivalent to $$\$$left(2x^3$$y^2$$\$$right)^3$?

Accepted Answer

$$8x^9y^6$

Question 2

Simplify $$\dfrac{27x^5$y^3$$}{$$9x^2y$$}$.

Accepted Answer

$$3x^3y^2$

Question 3

Which of the following is the correct simplification of $$\sqrt[3]{8x^6$y^9$$}$?

Accepted Answer

$$2x^2y^3$

Question 4

Solve the quadratic equation $$x^2 - 11x + 30 = 0$.

Accepted Answer

$$x = 5 or$$ $$x = 6$$

Question 5

Which of the following is NOT a function?

Accepted Answer

A relation where the input $$x = 2 is $$paired with both $$y = 3$$ and $$y = 5$$

Question 6

Find the domain of the function $$f(x) = \dfrac{3x + 2}{x - 4}.$$

Accepted Answer

$$(-\infty, 4) \cup (4, \infty)$$

Question 7

Given $$f(x) = 2x^2$ - 3x + 1$$, find $$f(x+1).$$

Accepted Answer

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

Question 8

Which of the following describes an even function?

Accepted Answer

$$f(-x) = f(x)$$ for all $$x in $$the domain

Question 9

If $$f(x) = |x|$$, which of the following statements is true?

Accepted Answer

$$f(x) is $$even

Question 10

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -5t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$22$$ meters

Question 11

Which transformation will shift the graph of $$f(x) to $$the right by $$3$$ units?

Accepted Answer

$$f(x-3)$$

Question 12

Given the piecewise function $$f(x) = \begin{cases} 3x+4 & x \u003c 0 \ 2x-1 & x \geq 0 \end{cases}$$, what is $$f(-2)$$?

Accepted Answer

$$-2$$

Question 13

Which of the following is the range of $$f(x) = x^2$ for x$$ \in [-2, 3]$$?

Accepted Answer

$$[0, 9]$$

Question 14

If $$g(x) = \sqrt{x-2}$$, what is the domain of $$g(x)$$?

Accepted Answer

$$[2, \infty)$$

Question 15

Which of the following is the correct factorization of $$x^2 - 16$?

Accepted Answer

$$(x+4)(x-4)$$

Question 16

A function $$h(x) is $$defined as $$h(x) = 3x + 36$$ for $$x \geq 12. $$What is the domain of $$h(x)$$?

Accepted Answer

$$[12, \infty)$$

Question 17

Which of the following describes a vertical stretch of $$f(x) by a $$factor of $$3$$?

Accepted Answer

$$3f(x)$$

Question 18

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

Accepted Answer

$$9$$

Question 19

Which of the following intervals represents where the function $$f(x) is $$increasing if $$f(x)$$ has a local minimum at $$x = 2$$ and a local maximum at $$x = 5$$?

Accepted Answer

$$(2, 5)$$

Question 20

Which of the following is the correct simplification of $$\left(\dfrac{x^3$y^2$$}{$$x^2y^5$}\$$right)^2$$?

Accepted Answer

$$x^2y$$^{-6}$

Precalculus Study Notes: Exponents, Roots, Quadratic Equations, Functions, and Graphs

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