Given the function $$g(x) = frac{1}{x - 2}$$, which of the following statements is true about the function's graph?

The function has a vertical asymptote at $$x = 2$$.

The function is undefined at $$x = 2$$.

The function has a hole in the graph at $$x = 2$$.

The function is continuous at $$x = 2$$.

Consider the function $$g(x) = frac{1}{x^2}$$. What is the domain of the function $$g(x)$$?

All real numbers except 0 and 1

All real numbers except -1 and 1

Consider the function $$f(x) = x^3 - 2x^2 + x + 1$$. What are the x-intercepts of the function $$f(x)$$?

$$x = -1$$, $$x = 1$$, and $$x = 2$$

$$x = -1$$, $$x = 1$$, and $$x = -2$$

$$x = -1$$, $$x = 1$$, and $$x = -3$$

$$x = -1$$, $$x = 1$$, and $$x = 3$$

FREE Digital SAT Maths Practice Set 5

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Question 1

Consider the function [Tex]f(x) = ax^2 + bx + c[/Tex], where [Tex]a[/Tex], [Tex]b[/Tex], and [Tex]c[/Tex] are constants. If the vertex of the parabola represented by [Tex]f(x)[/Tex] is located at the point [Tex](2, -3)[/Tex], and the parabola opens upwards, what is the value of [Tex]a[/Tex]?

1
2
-1
-2
Cannot be determined

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Question 2

Given the function [Tex]g(x) = \frac{1}{x - 2}[/Tex], which of the following statements is true about the function's graph?

The function is undefined at [Tex]x = 2[/Tex].
The function has a vertical asymptote at [Tex]x = 2[/Tex].
The function has a hole in the graph at [Tex]x = 2[/Tex].
The function is continuous at [Tex]x = 2[/Tex].
None of the above.

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Question 3

Consider the function [Tex]h(x) = \sqrt{x}[/Tex]. Which of the following statements about the domain and range of the function is true?

The domain of [Tex]h(x)[/Tex] is all real numbers, and the range is all non-negative real numbers.
The domain of [Tex]h(x)[/Tex] is all non-negative real numbers, and the range is all real numbers.
The domain of [Tex]h(x)[/Tex] is all real numbers, and the range is all real numbers.
The domain of [Tex]h(x)[/Tex] is all non-negative real numbers, and the range is all non-negative real numbers.
None of the above.

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Question 4

Consider the function [Tex]f(x) = 2x^2 - 4x + 3[/Tex]. What are the coordinates of the vertex of the parabola represented by [Tex]f(x)[/Tex]?

$(2, -5)$
$(2, 3)$
$(1, -2)$
$(1, 3)$
None of the above

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Question 5

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

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

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Question 6

Consider the function [Tex]g(x) = \frac{1}{x^2}[/Tex]. What is the domain of the function [Tex]g(x)[/Tex]?

All real numbers
All real numbers except 0
All real numbers except 1
All real numbers except 0 and 1
All real numbers except -1 and 1

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Question 7

Consider the function [Tex]f(x) = x^3 - 2x^2 + x + 1[/Tex]. What are the x-intercepts of the function [Tex]f(x)[/Tex]?

[Tex]x = -1[/Tex] and [Tex]x = 1[/Tex]
[Tex]x = -1[/Tex], [Tex]x = 1[/Tex], and [Tex]x = 2[/Tex]
[Tex]x = -1[/Tex], [Tex]x = 1[/Tex], and [Tex]x = -2[/Tex]
[Tex]x = -1[/Tex], [Tex]x = 1[/Tex], and [Tex]x = -3[/Tex]
[Tex]x = -1[/Tex], [Tex]x = 1[/Tex], and [Tex]x = 3[/Tex]

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Question 8

Which of the following equations has no real solutions?

[Tex]x^2 + 4x + 3 = 0[/Tex]
[Tex]x^2 - 4x + 4 = 0[/Tex]
[Tex]x^2 + 2x + 1 = 0[/Tex]
[Tex]x^2 - 6x + 9 = 0[/Tex]
[Tex]x^2 + 5x + 6 = 0[/Tex]

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Question 9

What is the solution to the equation [Tex]x^2 + 9 = 12x[/Tex]?

[Tex]x = 3[/Tex]
[Tex]x = 4[/Tex]
[Tex]x = 5[/Tex]
[Tex]x = 6[/Tex]
[Tex]x = 7[/Tex]

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Question 10

Which of the following equations has exactly one real solution?

[Tex]x^2 - 6x + 9 = 0[/Tex]
[Tex]x^2 - 4x + 4 = 0[/Tex]
[Tex]x^2 + 5x + 6 = 0[/Tex]
[Tex]x^2 - 3x + 2 = 0[/Tex]
[Tex]x^2 + 2x + 1 = 0[/Tex]

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