Question

the graph of a function f is given. use the horizontal-line test to determine whether f is one-to-one.

is f one-to-one?

○ no
○ yes

Explanation:

Step1: Recall Horizontal-Line Test

The horizontal - line test states that a function \( y = f(x) \) is one - to - one if and only if no horizontal line intersects the graph of \( f \) more than once.

Step2: Analyze the Given Graph

Looking at the provided graph (a curve that seems to be increasing, like an exponential or a strictly increasing function), when we imagine drawing horizontal lines across the graph, each horizontal line will intersect the graph at most once. This is because the function is strictly increasing (as the \( y \) - value increases as the \( x \) - value increases), and for a strictly increasing function, the horizontal - line test is passed.

Answer:

Yes