Question 1

Which of the following is the simplified form of $$\displaystyle \frac{2^5$ \cdot 2$$^{-3}$$}{2^2$}$$?

Accepted Answer

$$2^2$$

Question 2

A ball is thrown upward from the ground with an initial velocity of $$32 ft/s. $$Its height after $$t$$ seconds is given by $$h(t) = -16t^2$ + 32t. $$What is the maximum height the ball reaches?

Accepted Answer

$$16 ft$$

Question 3

Given the quadratic equation $$3x^2 - 2x - 8 = 0$, what are its solutions?

Accepted Answer

$$x = \frac{2 \pm \sqrt{100}}{6}$$

Question 4

Which of the following is the equation of the line passing through $$(2, -3)$$ with slope $$m = 4$$?

Accepted Answer

$$y = 4x - 11$$

Question 5

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

Accepted Answer

$$24$$

Question 6

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$ - 4$$

Question 7

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

Accepted Answer

$$x \geq 2$$

Question 8

Which of the following lines is perpendicular to $$y = -\frac{1}{2}x + 3$$?

Accepted Answer

$$y = 2x - 1$$

Question 9

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

Accepted Answer

$$7$$

Question 10

If $$f(x) = 3x - 5$$, find $$f^{-1}(x$$)$$, the inverse function.

Accepted Answer

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

Question 11

Which of the following best describes a one-to-one function?

Accepted Answer

Each $$y$$ value is paired with exactly one $$x$$ value.

Question 12

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

Accepted Answer

Question 13

Suppose $$f(x) = x^2$ and g(x) = x + 1$. What is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 14

Which of the following statements is true about the zeros of $$f(x) = (x-2)^3$(x+1)^2$?

Accepted Answer

$$x = 2 is a $$zero of multiplicity $$3.$$

Question 15

A function $$f is $$defined by the table: $$f(1) = 3$$, $$f(2) = 5$$, $$f(3) = 7. If$$ $$g(x) = 2x$$, what is $$(f + g)(2)$$?

Accepted Answer

$$9$$

Question 16

Which transformation maps the graph of $$y = x^2$ to y$$ = $$(x-3)^2 + 2$?

Accepted Answer

Shift right $$3$$ units, up $$2$$ units

Question 17

Given $$f(x) = x^3$ - x$$, determine if $$f is $$even, odd, or neither.

Accepted Answer

Odd

Question 18

If $$f(x) = \frac{1}{x}$$ and $$g(x) = x + 2$$, what is the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$x 
eq -2$$

Question 19

Which of the following functions passes the horizontal line test?

Accepted Answer

$$f(x) = x^3$

Precalculus Study Guide: Key Objectives Through Chapter 4.3

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