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

Key Concepts

Reflection Across the X-Axis

Reflecting a graph across the x-axis involves changing the sign of the output values (y-values) of the function. For a function ƒ(x), the reflection across the x-axis is represented by -ƒ(x). This means that for every point (x, y) on the original graph, the reflected point will be (x, -y).

Function Notation

Function notation is a way to represent a mathematical function in the form of ƒ(x), where 'ƒ' denotes the function and 'x' is the input variable. Understanding function notation is crucial for manipulating and transforming functions, such as finding reflections or translations. In this case, ƒ(x) = 3x - 4 is the original function we will transform.

Linear Functions

A linear function is a polynomial function of degree one, which can be 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. In this question, the function ƒ(x) = 3x - 4 is linear, and understanding its properties is essential for determining the equation of its reflection.