Consider the graph of the function $ f(x) = \left( \frac{1}{4} \right)^x $. Which statements describe key...

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Select all the correct answers.
Consider the graph of the function $ f(x) = \left( \frac{1}{4} \right)^x $.
Which statements describe key features of function $ f $?
☐ range of $ \{ y | 0 < y < \infty \} $
☐ x-intercept at $ (3, 0) $
☐ horizontal asymptote of $ y = 2 $
☐ horizontal asymptote of $ y = 0 $
☐ y-intercept at $ (0, 1) $
☐ domain of $ \{ x | -1 < x < \infty \} $

SnapAndSolve AI · Accepted Answer

Range of $ \{ y | 0 < y < \infty \} $: Correct. The range of the function $ f(x) = \left( \frac{1}{4} \right)^x $ is all positive real numbers. x-intercept at $ (3, 0) $: Incorrect. The function $ f(x) = \left( \frac{1}{4} \right)^x $ does not have an x-intercept because it never crosses the x-axis. Horizontal asymptote of $ y = 2 $: Incorrect. The horizontal asymptote is $ y = 0 $, not $ y = 2 $. Horizontal asymptote of $ y = 0 $: Correct. The function approaches $ y = 0 $ as $ x \to \infty $. y-intercept at $ (0, 1) $: Correct. When $ x = 0 $, $ f(x) = 1 $. Domain of $ \{ x | -1 < x < \infty \} $: Incorrect. The domain of the function is all real numbers $ \{ x | -\infty < x < \infty \} $.

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Consider the graph of the function \( f(x) = \left( \frac{1}{4} \right)^x \). Which statements describe key...

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