Question

The graph of $f\left(x\right)=x^2-4$and $g\left(x\right)=\left|x^2-4\right|$are shown. Explain how the graph of gobtained from the graph of f.

Short answer

We obtain the graph of $f\left(x\right)=\left|x^2-4\right|$by combining the graph $f\left(x\right)=x^2-4$and where$x>0.$

Step-by-step solution

Step 1. Concept of combining shifting of a function.

We have two transformations, we can combine them together. Vertical shifts are outside changes that effect the output y-axis values and shift the function up or down. Horizontal shift are inside changes that effect the input values and shift the function left or right. Combining the two types of shift will cause the graph of a function to shift up or down and right to left.

Step 2. Draw the given graph.

The given graph is,

Step 3. Answer the question.

We obtain the graph of $f\left(x\right)=\left|x^2-4\right|$by combining the graph $f\left(x\right)=x^2-4$and where$x>0.$