Problem preview
F-BF.3 Warmup M1-018-A05-V01

Analyze graph transformations caused by f(x)+k, kf(x), f(kx), and f(x+k); identify even/odd functions.

Describe reflection across the x-axis

Problem

Use the graph to describe the transformation from \(f(x)\) to \(-f(x)\), including its effect on coordinate values.

Big Picture

What this problem is really about

First locate the negative sign relative to the function, because an outside negative acts on outputs rather than inputs. We’ll translate that effect into a point-mapping rule, then use the paired points in the graph to see which coordinate stays fixed and which changes sign. Equal distances on opposite sides of an axis will identify the reflection.

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Four variants of this problem type
Curriculum context
Course
Math I
Standard
F-BF.3
Category
Functions
Domain
Building Functions
Objective
Analyze graph transformations caused by f(x)+k, kf(x), f(kx), and f(x+k); identify even/odd functions.
Problem type
Describe reflection across the x-axis