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

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; 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 and  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|

⇒

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;

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).

Since, k = -5 < 0

then;

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

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total amount to be paid = $19.5

step-by-step explanation:

given ,

original price = $25.99

discount = 25%

discount amount = 25% of original price

discount amount = 25/100   * 25.99

discount amount = $6.49

hence , the total amount to be paid = original price - discount amount

                                                            = $25.99 - $6.49

                                                            =$19.5

total amount to be paid = $19.5