Let ƒ(x) = 3x -4. Find an equation for each reflection of the graph of ƒ(x). across the y-axis

Key Concepts

Reflection Across the Y-Axis

Reflecting a graph across the y-axis involves transforming the function by replacing x with -x. For a function ƒ(x), the reflection is represented as ƒ(-x). This changes the sign of the x-coordinates of all points on the graph, effectively flipping it over the y-axis.

Linear Functions

A linear function is a polynomial function of degree one, typically expressed in the form ƒ(x) = mx + b, where m is the slope and b is the y-intercept. The graph of a linear function is a straight line, and understanding its properties is essential for analyzing transformations such as reflections.

Function Notation

Function notation, such as ƒ(x), is a way to denote a function and its output for a given input x. It allows for clear communication of mathematical ideas and operations. Understanding function notation is crucial for performing operations like finding reflections, as it helps in manipulating and interpreting the function correctly.