Question

How does the graph of y=|x|+ 4 compare to the graph of the parent function y=|x|?​

Answer 1

y=|x|+ 4 is a shift of 4 units up of the parent absolute value function y=|x|

How does the graph of y=|x|+ 4 compare to the graph of the parent function y=|x|?​

The transformations involved can be represented mathematically by g(x) = f(x) + 4, where g(x) is the shifted function and f(x) is the parent function. The addition of 4 represents the vertical shift.

So replacing f(x) = |x|

g(x) = f(x) +4

g(x)= |x| + 4

Answer 2

Please check the explanation and attached graph.

Explanation:

Given the parent function

y = |x|

In order to translate the absolute function y = |x| vertically, we can use the function

g(x) = f(x) + h

when h > 0, the graph of g(x) translated h units up.

Given that the image function

y=|x|+4

It is clear that h = 4. Since 4 > 0, thus the graph y=|x|+4 translated '4' units up.

The graph of both parent and translated function is attache below.

In the graph,

The blue line represents the parent function y=|x|.

The red line represents the image function y=|x| + 4.

It is clear from the graph that the y=|x| + 4 translated '4' units up.

Please check the attached graph.