Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to describe the graph the given function.

h(x) = 2 | x | + 2

Hey, I just did it.

Yeah sorry , I was trying to re post it so it would be easier for you to see it , But i seen that you replied , I replied back

so did I

To graph the function h(x) = 2 | x | + 2, let's start with the standard absolute value function f(x) = | x | and apply transformations step by step.

1. Graphing the standard absolute value function f(x) = | x |:
Start by plotting some points to create the graph of f(x) = | x |.
For positive x-values, f(x) is equal to x since the absolute value of x is x when x is positive.
For negative x-values, f(x) is equal to -x since the absolute value of x is -x when x is negative.
Connect the points and extend the graph in both directions to create a "V" shape that passes through the origin.

2. Applying the transformation h(x) = 2 | x | + 2:
To apply transformations to the graph of f(x), we need to understand the effect of each transformation:

a) Vertical stretch:
Multiplying the function by 2 vertically stretches the graph along the y-axis.
This means that the distance between the graph and the x-axis doubles, making the "V" shape narrower.

b) Vertical shift:
Adding 2 to the function vertically shifts the graph upwards by 2 units.
Every point on the graph will move up by 2 units.

By applying the vertical stretch and shift to the graph of f(x), we get the graph of h(x) = 2 | x | + 2.
The new graph will have a narrower "V" shape compared to the standard absolute value graph, and it will be shifted upward by 2 units.

Remember to label your axes and scales appropriately to have an accurate graph representation.