Question

graph the following function on the axes provided.
$f(x) = \

$$\begin{cases} x & \\text{for} & x < -4 \\\\ 1 & \\text{for} & x > 5 \\end{cases}$$

$
click and drag to make a line. click the line to delete it.
click on an endpoint of a line to change it.
graph axes with grid, x from -10 to 10, y from -10 to 10

Explanation:

Step1: Graph \( y = x \) for \( x < -4 \)

The function \( y = x \) is a straight line with a slope of 1. For \( x < -4 \), we consider points where \( x \) is less than -4. For example, when \( x = -5 \), \( y = -5 \); when \( x = -10 \), \( y = -10 \). We draw a line with an open circle at \( x = -4 \) (since \( x < -4 \), not including -4) and extend it to the left.

Step2: Graph \( y = 1 \) for \( x > 5 \)

The function \( y = 1 \) is a horizontal line. For \( x > 5 \), we consider points where \( x \) is greater than 5. For example, when \( x = 6 \), \( y = 1 \); when \( x = 10 \), \( y = 1 \). We draw a horizontal line with an open circle at \( x = 5 \) (since \( x > 5 \), not including 5) and extend it to the right.

Answer:

To graph the piecewise function:

• For \( x < -4 \), draw the line \( y = x \) (slope 1, open circle at \( (-4, -4) \), extending left).
• For \( x > 5 \), draw the horizontal line \( y = 1 \) (open circle at \( (5, 1) \), extending right).