Question

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Explanation:

Analyze the y-intercept of the logarithmic function

Using the Logarithmic Intercepts and Logarithmic Functions knowledge points

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Analyze the inverse function relationship

Using the Logarithmic and Exponential Inverses knowledge point

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Find the x-intercept of the logarithmic function

Using the Logarithmic Intercepts knowledge point

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Determine the limit behavior as x approaches 0 from the right

Using the Logarithmic Limits knowledge point

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Answer:

Question 1

Which of the following explains why \(f(x) = \log_4(x)\) does not have a \(y\)-intercept? Check all that apply.

• There is no power of 4 that is equal to 0 (Correct answer)
• There is no power of 4 that is equal to 1
• Its inverse does not have any x-intercepts (Correct answer)
• Its inverse does not have any y-intercepts

Question 2

The \(x\)-intercept of \(f(x) = \log_4(x)\) is <blank>1</blank>.

Question 3

What happens to the value of \(f(x) = \log_4(x)\) as \(x\) approaches 0 from the right?

• f(x) approaches negative infinity (Correct answer)
• f(x) approaches 0
• f(x) approaches infinity