Question 1

Which of the following best describes the end behavior of the function $$f(x) = x^3$ - 4x as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o \infty$$

Question 2

Given the graph of $$f(x) = x^2$ - 4x + 3$$, which of the following statements is true about its vertex?

Accepted Answer

The vertex is at $$(2, -1)$$

Question 3

Suppose a function $$f(x) is $$even. Which of the following must be true for its graph?

Accepted Answer

It is symmetric about the $$y-$$axis

Question 4

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

Accepted Answer

$$x \geq 2$$

Question 5

A real-world scenario: The height $$h (in $$meters) of a ball thrown upward from the ground is given by $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the maximum height reached by the ball?

Accepted Answer

$$21.95$$ meters

Question 6

Which of the following graphs represents an odd function?

Accepted Answer

A graph symmetric about the origin

Question 7

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

Accepted Answer

$$9$$

Question 8

Which of the following best describes the range of $$f(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

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

Which of the following functions has a vertical asymptote at $$x = 2$$?

Accepted Answer

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

Question 11

A function $$f(x) is $$defined as $$f(x) = |x-3|. $$What is the minimum value of $$f(x)$$?

Accepted Answer

$$0$$

Question 12

Which of the following is the inverse of $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-5}{2}$$

Question 13

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is (f$$ \circ g)(4)$$?

Accepted Answer

$$4$$

Question 14

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

Accepted Answer

Shift right by 3 units and up by 2 units

Question 15

A function $$f(x) is $$defined as $$f(x) = \frac{1}{x}. $$Which of the following statements is true?

Accepted Answer

The function is undefined at $$x = 0$$

Question 16

Which of the following is the correct graph for $$f(x) = -x^2$?

Accepted Answer

A downward opening parabola with vertex at the origin

Question 17

If $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, what is $$(f \circ g)(1)$$?

Accepted Answer

$$1$$

Question 18

Which of the following best describes the range of $$f(x) = x^2$ - 4x + 5$$?

Accepted Answer

$$[1, \infty)$$

Question 19

A piecewise function is defined as $$f(x) = \begin{cases} 2x+1 & x \u003c 1 \ x^2$ & x \geq 1 \end{cases}. $$What is $$f(0) + f(2)$$?

Accepted Answer

$$5$$

Question 20

Which of the following is the correct domain of $$f(x) = \frac{1}{\sqrt{x-1}}$$?

Accepted Answer

$$x \u003e 1$$

Graphing and Analyzing Functions in Calculus

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