Which of the following best describes the end behavior of the exponential function $$f(x) = 2^x$$ ?

As $$x \to \infty$$ , $$f(x) \to \infty$$ ; as $$x \to -\infty$$ , $$f(x) \to 0$$

As $$x \to \infty$$ , $$f(x) \to 0$$ ; as $$x \to -\infty$$ , $$f(x) \to \infty$$

As $$x \to \infty$$ , $$f(x) \to 0$$ ; as $$x \to -\infty$$ , $$f(x) \to 0$$

As $$x \to \infty$$ , $$f(x) \to -\infty$$ ; as $$x \to -\infty$$ , $$f(x) \to \infty$$

If $$f(x) = 5^x$$ and $$g(x) = \log_5(x)$$ , which statement is true?

$$f$$ and $$g$$ are not related

$$f$$ is the inverse of $$g$$ only for $$x > 0$$

$$f$$ and $$g$$ are both exponential functions

Which of the following is a characteristic of all exponential functions of the form $$f(x) = a^x$$ where $$a > 1$$ ?

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

The function is decreasing for all $$x$$

The function is undefined for $$x

The function passes through the point $$(0, 0)$$

Which of the following best describes the inverse of the graph of $$f(x) = \log_3(x)$$ ?

It is concave up and increasing.

It is concave up and decreasing.

It is concave down and increasing.

It is concave down and decreasing.

For the function $$f(x) = \ln(x)$$ , which of the following statements about its concavity is true?

It is concave down for all $$x > 0$$

It changes concavity at $$x = 1$$

It is concave up for all $$x > 0$$

It is neither concave up nor concave down

For the function $$f(x)=\ln(x)$$ , which of the following statements about the concavity of $$f^{-1}(x)$$ is true?

It is concave up for all x-values in its domain

It changes concavity at $$x = 1$$

It is concave down for all x-values in its domain

It is neither concave up nor concave down

Given the graph of $$f(x) = \log_2(x)$$ , what does the concavity of the function indicate about its rate of increase as $$x$$ becomes large?

The rate of increase slows down as $$x$$ increases

The function decreases for large $$x$$

The rate of increase remains constant

The rate of increase accelerates as $$x$$ increases

2.9-2.11 Exploring Exponential and Logarithmic Functions

Authored by Stefanie Frey

Mathematics

12th Grade

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Used 7+ times

2.9-2.11 Exploring Exponential and Logarithmic Functions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

GA.MA.9-12.AA.FGR.3.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

GA.MA.9-12.AA.FGR.3.1

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following graphs represents a logarithmic function?

A straight line passing through the origin

A parabola opening upwards

Tags

GA.MA.9-12.AA.FGR.3.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

All real numbers

Tags

GA.MA.9-12.AA.FGR.3.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

GA.MA.9-12.AA.FGR.3.1

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

GA.MA.9-12.AA.FGR.3.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

GA.MA.9-12.AA.FGR.3.1

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2.9-2.11 Exploring Exponential and Logarithmic Functions

Which of the following graphs represents a logarithmic function?

Make sure you notice that it provided f(x) but asked for the range of THE INVERSE of f .

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