a. Sketch the graph of y=|x| b. Sketch the graph of y=|x|+2 c. Sketch the graph of y=|x|-2 d. De

step 1 We're looking at f of x equals absolute value of x. And when you change the equation to f of x e

A. Sketch the graph of y=|x| b. Sketch the graph of y=|x|+2...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Graph Transformation

Graph transformation encompasses various operations such as scaling, shifting, reflecting, or rotating a graph. In the context of the absolute value function, transformations like vertical translation and horizontal shifts are common and help in understanding how altering the function's equation affects the graph's position and orientation in the coordinate plane.

Vertical Translation

Vertical translation refers to moving the graph of a function up or down by a constant amount. For example, adding a constant a to the absolute value function, as in y = |x| + a, shifts the graph upwards if a is positive and downwards if a is negative, without altering the horizontal position or shape of the graph.

Absolute Value Function

The absolute value function, expressed as y = |x|, forms a V-shaped graph with the vertex at the origin. It outputs the non-negative value of x, which means the function is defined piecewise as x for x ? 0 and -x for x < 0. This function is fundamental in understanding basic graph shapes and piecewise definitions in mathematics.

Transcript

Please give Ace some feedback