of 25 Which of these statements is true for $ f(x) = \left( \frac{1}{3} \right)^x $?

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Question 22 of 25
Which of these statements is true for $ f(x) = \left( \frac{1}{3} \right)^x $?
A. The graph contains $ (1, \frac{1}{3}) $.
B. The domain of $ f(x) $ is $ x > 0 $.
C. It is always increasing.
D. The range of $ f(x) $ is $ y > \frac{1}{10} $.

SnapAndSolve AI · Accepted Answer

A. The graph contains $ (1, \frac{1}{3}) $. This statement is true because when $ x = 1 $, $ f(x) = \left( \frac{1}{3} \right)^1 = \frac{1}{3} $. B. The domain of $ f(x) $ is $ x > 0 $. This statement is false. The domain of $ f(x) = \left( \frac{1}{3} \right)^x $ is all real numbers, $ x \in \mathbb{R} $. C. It is always increasing. This statement is false. The function $ f(x) = \left( \frac{1}{3} \right)^x $ is a decreasing exponential function. D. The range of $ f(x) $ is $ y > \frac{1}{10} $. This statement is false. The range of $ f(x) = \left( \frac{1}{3} \right)^x $ is $ y > 0 $.

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of 25 Which of these statements is true for \( f(x) = \left( \frac{1}{3} \right)^x \)?

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