Question

What is the range of the function y = 2 e Superscript x Baseline minus 1
all real numbers less than –1
all real numbers greater than –1
all real numbers less than 1
all real numbers greater than 1

Answer 1

y = 2e^x − 1. Since e^x > 0 for all x, 2e^x > 0 so 2e^x − 1 > −1. As x → −∞ the expression approaches −1 but never equals it.

Range: all real numbers greater than −1 (−1, ∞).