Question

8 - 13. describe the difference between the graphs of $y = x^{3}-x$ and $y = x^{3}-x + 5$. homework help

Explanation:

Step1: Recall the transformation rule

For a function \(y = f(x)\) and \(y=f(x)+k\), when \(k>0\), the graph of \(y = f(x)+k\) is the graph of \(y = f(x)\) shifted up by \(k\) units.

Let \(f(x)=x^{3}-x\). Then the first function is \(y = f(x)\) and the second function is \(y=f(x)+5\).

Step2: Apply the transformation rule

Since \(k = 5>0\), the graph of \(y=x^{3}-x + 5\) is the graph of \(y=x^{3}-x\) shifted up by \(5\) units.

Answer:

The graph of \(y=x^{3}-x + 5\) is the graph of \(y=x^{3}-x\) shifted up by \(5\) units.