Question

graph the function.

$r(x) = \

$$\begin{cases} \\ \\ x^2 - 1\\ \\text{ for } x \\leq 1\\\\ \\ \\ 5x - 5\\ \\text{ for } x > 1 \\end{cases}$$

$

part: 0 / 5

part 1 of 5

the first rule defines a select with vertex ( , ).

Explanation:

Step1: Identify function type

The first rule is $r(x)=x^2-1$, a quadratic function (parabola).

Step2: Find vertex of parabola

For $y=ax^2+bx+c$, vertex $x=-\frac{b}{2a}$. Here $a=1, b=0$, so $x=0$. Substitute $x=0$: $r(0)=0^2-1=-1$.

Answer:

quadratic function (parabola); $(0, -1)$