Question

graph the function.

\
(x) = \

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

\\

part: 0 / 5

part 1 of 5

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

Explanation:

Identify the first rule of the piecewise function

Using the Piecewise Functions knowledge point

$$ r(x) = -x^2 + 1 \quad \text{for} \quad x \le 1 $$

The equation \(y = -x^2 + 1\) is a quadratic function, which represents a parabola.

Determine the vertex of the parabola

Using the Parabola Vertex knowledge point

$$
LATEXBLOCK0
$$

Answer:

The first rule defines a parabola with vertex \((0, 1)\).