Question
Sketch the graph and give the domain and range of the function.$$f(x)=\left\{\begin{array}{ll}x^{2}+2, & x \leq 0 \\2-x^{2}, & x>0\end{array}\right.$$
Step 1
It is a piecewise function, which means it is defined by different expressions for different parts of its domain. For $x \leq 0$, the function is defined as $x^{2}+2$, and for $x > 0$, the function is defined as $2-x^{2}$. Show more…
Show all steps
Your feedback will help us improve your experience
Nick Johnson and 57 other Algebra educators are ready to help you.
Ask a new question
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
Sketch the graph and give the domain and range of the function. $$f(x)=\left\{\begin{aligned} x^{2}, & x \leq 0 \\ 1-x, & x>0 \end{aligned}\right.$$
Precalculus Preview
Functions
Sketch the graph and give the domain and range of the function. $$f(x)=\left\{\begin{array}{cl} x^{2}, & x<0 \\ -1, & 0<x<2 \\ x, & 2<x \end{array}\right.$$
Sketch the graph and give the domain and range of the function. $$f(x)=\left\{\begin{aligned} 1+x, & 0 \leq x \leq 1 \\ x, & 1<x<2 \\ \frac{1}{2} x+1, & 2 \leq x \end{aligned}\right.$$
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD