Question 1

Which of the following best describes the graph of the function $$f(x) = |x| as $$shown in the first image?

Accepted Answer

A V-shaped graph opening upwards with vertex at $$(0,0)$$

Question 2

Given the function $$f(x) = x^2$ - 4x + 3$$, what are its zeros?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 3

Which of the following is the correct vertex of the parabola $$y = -x^2$ + 4x - 3 as $$shown in the second image?

Accepted Answer

$$(2, 1)$$

Question 4

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

Accepted Answer

$$[0, \infty)$$

Question 5

Which of the following expressions is equivalent to $$\sqrt{9x^2$}$$?

Accepted Answer

$$3|x|$$

Question 6

Given the quadratic function $$f(x) = ax^2$ + bx + c$$, which formula gives the $$x-$$coordinate of the vertex?

Accepted Answer

$$x = -\frac{b}{2a}$$

Question 7

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

Accepted Answer

$$(x+2)^2$$

Question 8

Which of the following is the correct solution set for $$x^2 = 9$?

Accepted Answer

$$\{ -3, 3 \}$$

Question 9

If $$f(x) = \sqrt{x-1}$$, what is the domain of $$f$$?

Accepted Answer

$$[1, \infty)$$

Question 10

Which of the following is the correct factorization of $$x^2 - 4$?

Accepted Answer

$$(x-2)(x+2)$$

Question 11

If $$f(x) = x^2$ - 6x + 8$$, what are the zeros of $$f(x)$$?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 12

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

Accepted Answer

$$x = 25$$

Question 13

If $$f(x) = |x-3|$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$0$$

Question 14

Which of the following is the correct solution set for $$x^2 - 5x + 6 = 0$?

Accepted Answer

$$\{2, 3\}$$

Question 15

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

Accepted Answer

$$36$$

Question 16

Which of the following is the correct solution to $$x^2 = -4$?

Accepted Answer

$$x = 2i$$ and $$x = -2i$$

Question 17

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

Accepted Answer

$$(1, 0)$$

Question 18

Which of the following is the correct solution to $$|x| = 7$$?

Accepted Answer

$$x = 7 or$$ $$x = -7$$

Question 19

If $$f(x) = x^2$ + 2x + 1$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$0$$

Question 20

Which of the following is the correct solution to $$\sqrt{x+4} = 3$$?

Accepted Answer

$$x = 5$$

Fundamental Functions and Their Graphs: Study Notes for Business Calculus

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