Question

describe how the graphs of y=|x| and y=|x+5| are related.

Answer 1

Y=║x║is the parent function of y=║x+5║and y=║x+5║is the result of the parent function going through a transformation of horizontal shift left 5 units.

Answer 2

Answer:

To describe the graph y= |x| and y= |x+5| are related.

Modulus function state that the 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|.

then,

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.

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

then, substitute the value of y=0 and solve for x.

For the function y = |x|

to find the x-intercepts:

substitute value of y=0 we get;

0 = |x|

⇒$x = 0$

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

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

Find: x-intercept

substitute the value of y =0 we get;

$0 = |x+5|$

by definition of modulus function:

x+5 = 0 and -(x+5)=0

we get;

x = -5

Therefore, the x-intercept of the function y=|x+5| is, (-5, 0)

Translation:

To translate the absolute value function f(x)=| x | horizontally, you can use the function  

g(x)=f(x−k).

• If k>0, the graph of f(x) is translated k units to the right to get g(x).

• if k <0,  the graph of f(x) is translated k units to the left to get g(x).

Since, k = -5 < 0

then;

$g(x) = f(x+5) =|x+5|$

therefore, the graph y=|x| is translated 5 units to the left to get, y=|x+5|