Question

the range of f(x) = 5·2^x is all positive real numbers. a. true b. false

Explanation:

Step1: Analyze the function \( F(x) = 5 \cdot 2^x \)

The exponential function \( 2^x \) has a range of \( (0, +\infty) \) because for any real number \( x \), \( 2^x > 0 \).

Step2: Determine the range of \( 5 \cdot 2^x \)

When we multiply \( 2^x \) by 5 (a positive constant), the inequality \( 2^x > 0 \) becomes \( 5 \cdot 2^x > 0 \) (since multiplying a positive number by a positive constant keeps it positive). So the range of \( F(x) = 5 \cdot 2^x \) is all positive real numbers.

Answer:

A. True