Question

What is the range of the function y=e* + 1 graphed below?

Answer 1

`$f: \mathbb{R} \rightarrow \mathbb{R}, f(x) = e^(x) + 1$`

`\text{Range}(f) = \{y \in \mathbb{R} \vert x \in \mathbb{R}, f(x) = y\}`

`\text{Suppose $f(x) = a$}\\e^(x) + 1 = a \implies e^(x) = a - 1 \implies x = \ln(a-1)\\`

`\text{For the logarithm to be real, it must be true that $a - 1 > 0$}\\\text{But then we have that } a > 1. \implies \boxed{\text{Range}(f) = (1, \infty)}`

Answer 2

The answer is D. y > 1 on edge