Question
Use a graphing utility to graph the three functions in the same viewing window. Describe the graphs of $g$ and $h$ relative to the graph of $f$.$$\begin{aligned}&f(x)=x^{3}-3 x^{2}+2\\&g(x)=f(x-1)\\&h(x)=f(3 x)\end{aligned}$$
Step 1
Using a graphing utility, we can plot the points and connect them to get the graph of $f(x)$. The graph of $f(x)$ is a cubic function that opens upward. It has a local maximum at $x=1$ and a local minimum at $x=2$. The graph intersects the $x$-axis at $x=1$ and Show more…
Show all steps
Your feedback will help us improve your experience
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Use a graphing utility to graph the three functions in the same viewing window. Describe the graphs of $g$ and $h$ relative to the graph of $ÂŁ$. $$\begin{array}{l} f(x)=x^{3}-3 x^{2} \\ g(x)=-\frac{1}{3} f(x) \\ h(x)=f(-x) \end{array}$$
Functions and Their Graphs
Shifting, Reflecting, and Stretching Graphs
Use a graphing utility to graph the three functions in the same viewing window. Describe the graphs of $g$ and $h$ relative to the graph of $f$.$$\begin{aligned}&f(x)=x^{3}-3 x^{2}\\&g(x)=-\frac{1}{3} f(x)\\&h(x)=f(-x)\end{aligned}$$
Use a graphing utility to graph the three functions in the same viewing window. Describe the graphs of $g$ and $h$ relative to the graph of $f$.$$\begin{aligned}&f(x)=x^{3}-3 x^{2}\\&g(x)=f(x+2)\\&h(x)=\frac{1}{2} f(x)\end{aligned}$$
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD