Question

graph this function.

$f(x)=\

$$\begin{cases}-5x + 5&\\text{if }x\\leq1\\\\5x - 5&\\text{if }x>1\\end{cases}$$

$

select points on the graph to plot them. select \poi open.

Explanation:

Step1: Find points for \( x\leq1 \)

Substitute \( x = 0 \) into \( y=-5x + 5 \): \( y=-5(0)+5 = 5 \), so point \((0,5)\).
Substitute \( x = 1 \) into \( y=-5x + 5 \): \( y=-5(1)+5 = 0 \), so point \((1,0)\).

Step2: Find points for \( x>1 \)

Substitute \( x = 2 \) into \( y = 5x-5 \): \( y=5(2)-5=5 \), so point \((2,5)\).

Step3: Plot the points

For \( y=-5x + 5\) (\(x\leq1\)): draw a line segment (including the endpoint at \(x = 1\)).
For \( y=5x-5\) (\(x>1\)): draw a ray starting at \(x = 1\) (with an open - circle at \(x = 1\) for this part of the function since \(x>1\) for this sub - function).

Answer:

Plot the points \((0,5)\), \((1,0)\) (closed - circle for \(y=-5x + 5\) at \(x = 1\)), and \((2,5)\) (and other relevant points). Draw the line \(y=-5x + 5\) for \(x\leq1\) (including \((1,0)\)) and the line \(y = 5x-5\) for \(x>1\) (not including \((1,0)\) for this part).