Answer
Number 1
The graph of y = |x - 1| is presented below
Number 2
The graph of y = |x + 4| is presented below
Step-by-step explanation
To plot the graphs for absolute value functions that are linear functions, we just need to find the value of x when y = 0 and plot the graph from that point outwards to the right and left, with the slope of the given equation if it wasn't an absolute value function
Number 1
y = |x - 1|
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
So, Slope = 1 (to the right)
Slope = -1 (to the left)
when y = 0
0 = x - 1
x = 1
So, the starting point for the graph will be at (1, 0)
We will use the slopes to draw out the lines either side of this starting point.
The graph of this absolute value function is presented above under 'Answer'.
2) y = |x + 4|
Slope = 1 (to the right)
Slope = -1 (to the left)
when y = 0
y = x + 4
0 = x + 4
x = -4
So, the starting point for the graph will be at (-4, 0)
We will use the slopes to draw out the lines either side of this starting point.
The graph of this absolute value function is presented above under 'Answer'.
Hope this Helps!!!