Question

graph the function.

\
(x) = \

$$\begin{cases} x^2 - 4 & \\text{for } x \\le 2 \\\\ 2x - 4 & \\text{for } x > 2 \\end{cases}$$

\\

part: 0 / 5

part 1 of 5

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

Explanation:

Identify the first rule of the piecewise function

Using the Piecewise Functions knowledge point
The piecewise function is defined as:

$$ r(x) =
LATEXBLOCK0
$$

The first rule is \(y = x^2 - 4\), which is a quadratic function. Its graph is a parabola.

Determine the vertex of the parabola

Using the Parabola Vertex knowledge point

$$
LATEXBLOCK1
$$

Answer:

The first rule defines a <blank>parabola</blank> with vertex <blank>\((0, -4)\)</blank>.