In Exercises 7–10, determine from its graph if the function is...

Question

In Exercises 7–10, determine from its graph if the function is one-to-one.

f(x) = 1 - x/2, x ≤ 0

x/(x + 2), x > 0

Accepted Answer

Welcome back, everyone. Determine whether the function graph below is 121 or not. A says 12 1 and B says not 121. So for this problem, let's remember the horizontal line test. According to the horizontal line test. A function is not 1 to 1 if we can have at least one horizontal line that crosses the graph of the function at more than 1 point. If we can only identify one point for each horizontal line or basically no points, then our function is 1 to 1. So in this case, we have a piecewise function. It consists of two fragments. If we visually inspect the possible horizontal lines, we control horizontal lines that do not intersect the graph at all, so that's fine. Let's focus on the function itself given in red. If we keep drawing horizontal lines, we have one intersection point for one line, one intersection point for another, only one intersection point for the next line, and so on, right? So we can basically keep drawing those horizontal lines. And we can see that for every horizontal line drawn, we only have one. Point of intersection or no points at all, meaning the correct answer for this problem is a 121 based on the horizontal line test. Thank you for watching.

In Exercises 7–10, determine from its graph if the function is one-to-one.f(x) = 1 - x/2, x ≤ 0x/(x + 2), x > 0

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In Exercises 7–10, determine from its graph if the function is one-to-one.
f(x) = 1 - x/2, x ≤ 0
x/(x + 2), x > 0