Question

graph the function.

\
(x) = \

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

\\

part 1 of 5
the first rule defines a parabola with vertex \\((0, -4)\\).

part 2 of 5
since \\(x \le 2\\), the rightmost point \\((2, 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

$$ r(x) =
LATEXBLOCK0
$$

The second rule is \(y = 2x - 4\).

Determine the shape, slope, and y-intercept

The equation \(y = 2x - 4\) is in slope-intercept form \(y = mx + b\).

• The shape is a line.
• The slope \(m\) is \(2\).
• The y-intercept is \((0, -4)\).

Answer:

The second rule defines a <blank>line</blank> with slope <blank>2</blank> and y-intercept <blank>\((0, -4)\)</blank>.