Question

graph the function.

\
(x) = \

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

\\

part 1 of 5
the first rule defines a parabola with vertex \\((0, 1)\\).

part 2 of 5
since \\(x \le 1\\), the rightmost point \\((1, 0)\\) is graphed as a solid dot.

part 3 of 5
the second rule defines a select with slope and \\(y\\)-intercept \\(( , )\\).

Explanation:

Identify the second rule of the piecewise function

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

$$ r(x) =
LATEXBLOCK0
$$

The second rule is \(y = 5x - 5\).

Analyze the properties of the second rule

Using the Linear Function Properties knowledge point
The equation \(y = 5x - 5\) is in slope-intercept form \(y = mx + b\):

• The graph is a line.
• The slope \(m\) is \(5\).
• The \(y\)-intercept is \((0, -5)\).

Answer:

The second rule defines a <blank>line</blank> with slope <blank>5</blank> and \(y\)-intercept <blank>\((0, -5)\)</blank>.