Think about how the function changes when adding a constant value to the output. Recalling the slope-intercept form of a line might help as well.
See solution.
Practice makes perfect
We are asked to explain how the relationship between y =|x| and y=|x|+k is similar to the one between y = mx and y = mx + b. Let's start by recalling the slope-intercept form of a line.
y = mx + b
Here, m is the slope of the line and b is the y-intercept. Let's compare the slope and y-intercept of the given functions.
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Function & Slope & y-intercept
y= mx+ b & m & b
y= mx & m & 0
We see that both functions have the same slope m. Looking at the y-intercepts, and supposing that b>0, we can say that the graph of y=mx+b is a translation up b units of the graph of y=mx.
In a similar way, the graph for y =|x| will not have its V shape affected by adding a constant value k to the output. Therefore, the graph of y=|x|+k is a translation up k units of the graph of its parent function y=|x|.
In the case of linear functions, if b<0, then the graph of y=mx+b is a translation down b units of the graph of y=mx. Similarly, for absolute value functions, the graph of y=|x|+k is a translation down k units of the graph of y=|x|, if k<0.
