determining the domain and range of a piecewise function\nthe graph represents the piece - wise…
determining the domain and range of a piecewise function\nthe graph represents the piece - wise function:\nf(x)=\n\\begin{cases}x, & x > 0 \\\\0, & x = 0 \\\\-x, & x < 0\\end{cases}\nwhat is the domain and range of the function?\ndomain:\nrange:
Answer
Answer:
Domain: All real numbers (or $(-\infty,\infty)$) Range: $[0,\infty)$
Explanation:
Step1: Analyze domain of piece - wise function
The function is defined for $x>0$, $x = 0$ and $x<0$. So domain is all real numbers.
Step2: Analyze range of piece - wise function
When $x>0$, $y=x>0$. When $x = 0$, $y = 0$. When $x<0$, $y=-x>0$. So range is $y\geq0$ or $[0,\infty)$.