Question

The values on the x-axis range from negative 5 to 5 in increments of 1. The values on the y-axis range from 0 to 5 in increments of 1. A dotted line is labeled f left parenthesis x right parenthesis equals x plus 2. It begins in quadrant 3 sloping upward from left to right. The line passes through quadrant 2 and then rises through quadrant 1. It passes through left parenthesis negative 2 comma 0 right parenthesis, left parenthesis negative 1 comma 1 right parenthesis, and left parenthesis 3 comma 5 right parenthesis. A solid curve is labeled g left parenthesis x right parenthesis equals 2 superscript x baseline plus 1. It begins in quadrant 2 sloping upward from left to right and rises through quadrant 1. The curve passes through left parenthesis negative 5 comma 1 right parenthesis, left parenthesis 0 comma 2 right parenthesis, and left parenthesis 2 comma 5 right parenthesis. The curve and the line intersect at two points: left parenthesis 0 comma 2 right parenthesis and left parenthesis 1 comma 3 right parenthesis. All values are approximate.

Compare the functions graphed. What is true about the functions?

(1 point)

The curved function has two y
-intercepts, but the straight function has only 1.

One is a curve and the other is a line, but the y
-values of both functions increases as x
increases.

Answer 1

The second statement is true.

Reason: The first statement is false — a function can have at most one y‑intercept; both f(x)=x+2 and g(x)=2^x+1 have exactly one y‑intercept (f(0)=2 and g(0)=2). Both functions are increasing: the line has positive slope 1, and the exponential with base 2 (>1) rises as x increases.