Question

Graph the piecewise function below

h(x) = { y= 3x + 2 if -2 < x < 1

y= 1/2x - 1 if x < -2

What is domain? (Interval notation)

What is range? (Interval notation)

Answer 1

$h(x) = \begin{cases} y= 3x + 2 &\text{if } -2 < x < 1 \\ y= \frac{1}{2}x - 1 &\text{if } x < -2 \end{cases}\\$

Now, domain for the given function is $x\in$ $(-\infty,-2)\cup(-2,1)$ [From graph]

At $x=1,$ we get $y=5$

Range is $(-\infty,-4)\cup(-4,-2)\cup(-2,5)$