Question

Below are the functions of y=|x| and y=|x|-5 how are the functions related.

A. the functions have the same shape. the y-intercept of y=|x| is 0, and the y-intercept of the second function is 5.
B. the functions have the same y-intercept. the second function is steeper than y=|x|.
C. the two functions are the same.
D. the functions have the same shape. the y-intercept of y=|x| is 0, and the y-intercept of the second function is -5.

Answer 1

D. the functions have the same shape. the y-intercept of y=|x| is 0, and the y-intercept of the second function is -5

Answer 2

Option D is correct.

The functions have the same shape.

The y-intercepts of y=|x| is 0, and the y-intercepts of the second function y=|x|-5 is, -5

Explanation:

Modulus function state that a function which gives a positive output irrespective of the input.

The graph of the functions as shown below in the attachment :

The functions are;
`y= |x| -5` makes a "V'" shape much like y=|x|.

Every absolute value graph will take this same shape, as long as the expression inside the absolute value is linear.

therefore, these functions
`y= |x|` and
`y= |x| -5` have the same shape.

y-intercepts defined as the graph crosses the y-axis

i.e substitute the value of x=0 and solve for y.

For the function y = |x|

to find the y-intercepts:

substitute value of x =0 we get;

y = |0| = 0

Then, the y-intercept of the function y=|x| is 0.

Similarly, for the function y = |x|-5

Find: y-intercept

substitute the value of x =0 we get;

y = |0| - 5 = -5

Therefore, the y-intercept of the function y=|x|-5 is -5