Given the function $$g(x) = frac{1}{x}$$, which of the following statements is true about the function's graph?

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

The function has a horizontal asymptote at $$y = 0$$.

The function has a hole in the graph at $$x = 0$$.

The function is continuous at $$x = 0$$.

Consider the function $$h(x) = |x|$$. What are the x-values where the graph of $$h(x)$$ intersects the x-axis?

$$x = -1$$, $$x = 0$$, and $$x = 1$$

Given the function $$g(x) = frac{1}{x + 3}$$, which of the following statements is true about the function's graph?

The function is undefined at $$x = -3$$.

The function has a vertical asymptote at $$x = -3$$.

The function has a hole in the graph at $$x = -3$$.

The function is continuous at $$x = -3$$.

Given the function $$g(x) = frac{1}{x + 3}$$, which of the following statements is true about the function's graph?

The function is undefined at $$x = -3$$.

The function has a vertical asymptote at $$x = -3$$.

The function has a hole in the graph at $$x = -3$$.

The function is continuous at $$x = -3$$.

FREE Digital SAT Maths Practice Set 4

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Question 1

Given the function [Tex]g(x) = \frac{1}{x}[/Tex], which of the following statements is true about the function's graph?

The function is undefined at [Tex]x = 0[/Tex].
The function has a horizontal asymptote at [Tex]y = 0[/Tex].
The function has a hole in the graph at [Tex]x = 0[/Tex].
The function is continuous at [Tex]x = 0[/Tex].
None of the above.

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Question 2

Consider the function [Tex]h(x) = |x|[/Tex]. What are the x-values where the graph of [Tex]h(x)[/Tex] intersects the x-axis?

[Tex]x = 0[/Tex] only
[Tex]x = 0[/Tex] and [Tex]x = 1[/Tex]
[Tex]x = -1[/Tex] and [Tex]x = 1[/Tex]
[Tex]x = -1[/Tex] and [Tex]x = 0[/Tex]
[Tex]x = -1[/Tex], [Tex]x = 0[/Tex], and [Tex]x = 1[/Tex]

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Question 3

Which of the following functions represents a parabola that opens upward?

[Tex]f(x) = -x^2 - 4x - 3[/Tex]
[Tex]f(x) = -2x^2 + 4x - 1[/Tex]
[Tex]f(x) = 3x^2 - 2x + 5[/Tex]
[Tex]f(x) = 4x^2 - 2x + 1[/Tex]
[Tex]f(x) = -x^2 + 3x - 2[/Tex]

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Question 4

Consider the function [Tex]f(x) = x^2 + 4x + 4[/Tex]. What are the coordinates of the vertex of the parabola represented by [Tex]f(x)[/Tex]?

$(-2, 0)$
$(2, 0)$
$(4, 0)$
$(-4, 0)$
None of the above

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Question 5

Given the function [Tex]g(x) = \frac{1}{x + 3}[/Tex], which of the following statements is true about the function's graph?

The function is undefined at [Tex]x = -3[/Tex].
The function has a vertical asymptote at [Tex]x = -3[/Tex].
The function has a hole in the graph at [Tex]x = -3[/Tex].
The function is continuous at [Tex]x = -3[/Tex].
None of the above.

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Question 6

Given the function [Tex]g(x) = \frac{1}{x + 3}[/Tex], which of the following statements is true about the function's graph?

The function is undefined at [Tex]x = -3[/Tex].
The function has a vertical asymptote at [Tex]x = -3[/Tex].
The function has a hole in the graph at [Tex]x = -3[/Tex].
The function is continuous at [Tex]x = -3[/Tex].
None of the above.

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Question 7

Which of the following equations has two distinct real solutions?

[Tex]x^2 - 4x + 4 = 0[/Tex]
[Tex]x^2 - 6x + 9 = 0[/Tex]
[Tex]x^2 + 3x + 3 = 0[/Tex]
[Tex]x^2 - 2x + 1 = 0[/Tex]
[Tex]x^2 + 2x + 2 = 0[/Tex]

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Question 8

What is the solution to the equation [Tex]x^2 - 2x - 8 = 0[/Tex]?

[Tex]x = -2[/Tex] or [Tex]x = 4[/Tex]
[Tex]x = -4[/Tex] or [Tex]x = 2[/Tex]
[Tex]x = -1[/Tex] or [Tex]x = 8[/Tex]
[Tex]x = -4[/Tex] or [Tex]x = 6[/Tex]
[Tex]x = -1[/Tex] or [Tex]x = 4[/Tex]

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Question 9

Which of the following expressions is equivalent to [Tex]3(x - 2)^2[/Tex]?

[Tex]3x^2 - 12[/Tex]
[Tex]3x^2 - 12x + 12[/Tex]
[Tex]3x^2 - 12x + 9[/Tex]
[Tex]9x^2 - 24x + 12[/Tex]
[Tex]9x^2 - 12x + 9[/Tex]

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Question 10

Which of the following expressions is equivalent to [Tex]\frac{{6x - 12}}{{3x}}[/Tex]?

[Tex]2x - 4[/Tex]
[Tex]2x - 6[/Tex]
[Tex]x - 2[/Tex]
[Tex]x - 4[/Tex]
[Tex]x - 6[/Tex]

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