Which of the following statements is true about the function $$f(x) = x^3$$ ?

The domain is all real numbers, and the range is $$[0, \infty)$$ .

The domain is $$[0, \infty)$$ , and the range is all real numbers.

The domain is $$[0, \infty)$$ , and the range is $$[0, \infty)$$ .

Compare the properties of the functions $$f(x) = x^2$$ and $$g(x) = 2^x$$ .

$$f(x)$$ is a polynomial function, and $$g(x)$$ is an exponential function.

Both functions are increasing for all $$x$$ .

Which of the following statements is true about the function $$f(x) = \sqrt{x}$$ ?

The domain is $$[0, \infty)$$ , and the range is $$[0, \infty)$$ .

The domain is all real numbers, and the range is $$[0, 1]$$ .

The domain is $$[0, 1]$$ , and the range is $$[0, \infty)$$ .

Compare the properties of the functions $$f(x) = \ln(x)$$ and $$g(x) = e^x$$ .

$$f(x)$$ is a logarithmic function, and $$g(x)$$ is an exponential function.

Both functions are increasing for all $$x$$ .

Identify the effect on the graph of $$f(x) = x^2$$ when it is replaced by $$f(2x)$$ .

The graph shifts 2 units to the right.

The graph shifts 2 units to the left.

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

The domain is all real numbers except 0, and the range is all real numbers except 0.

The domain is $$[0, \infty)$$ , and the range is $$[0, \infty)$$ .

The domain is $$(-\infty, 0]$$ , and the range is $$(-\infty, 0]$$ .

Compare the properties of the functions $$f(x) = \sin(x)$$ and $$g(x) = \cos(x)$$ .

$$f(x)$$ is an odd function, and $$g(x)$$ is an even function.

Both functions are increasing for all $$x$$ .

Identify the effect on the graph of $$f(x) = x^2$$ when it is replaced by $$f(x - 2)$$ .

The graph shifts 2 units to the right.

The graph shifts 2 units to the left.

Which of the following statements is true about the function $$f(x) = e^x$$ ?

The domain is all real numbers, and the range is $$(0, \infty)$$ .

The domain is $$[0, \infty)$$ , and the range is $$[0, \infty)$$ .

The domain is $$(-\infty, 0]$$ , and the range is $$(-\infty, 0]$$ .

Compare the properties of the functions $$f(x) = x^2$$ and $$g(x) = x^3$$ .

$$f(x)$$ is an even function, and $$g(x)$$ is an odd function.

Both functions are increasing for all $$x$$ .

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Authored by Alissar Talhouk

Mathematics

12th Grade

CCSS covered

Used 3+ times

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31 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.HSA.REI.B.4

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The graph shifts 3 units to the left.

The graph shifts 3 units to the right.

The graph shifts 3 units up.

The graph shifts 3 units down.

Tags

CCSS.HSF.BF.B.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.HSF.BF.B.4

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The domain is all real numbers, and the range is all real numbers.

Tags

CCSS.HSF.IF.A.1

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Both functions have the same range.

Both functions have the same domain.

Tags

CCSS.HSF.IF.C.9

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.HSA.REI.B.4

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The graph becomes wider.

The graph becomes narrower.

The graph shifts 2 units up.

The graph shifts 2 units down.

Tags

CCSS.HSF.BF.B.3

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