Question

I need some help with this too please. Thanks?!!

Answer 1

Basically, you construct the original graph, then describe what happens to it when the equation is changed as indicated.

Explanation:

The initial graph looks like a symmetric "V" with the ends up and the point at (x,y) = (0,0).

WHAT does the second function do do it?
It multiplies it by 2, so we would expect the values to double. It then "shifts" it by 2 'y' values so the point is no longer at (0,0), but at (0,2).

So, the basic shape is unchanged, but it has been shifted to the right from zero, but still minimum on the x-axis, and the rate of it's increase, or opening is twice as much.

Answer 2

Compress and translation

Explanation:

If we first take `2|x|`, the 2 will multiply every 'x' value by two which means that the output 'y' will always be twice the value of 'x'. For example, when `x=1/2` we would see that y is equal to 1 and therefore, the graph is being stretched in the x-axis by a factor of `1/2`.

Looking at the `+2` now, since it would add two to all of the original output values, that means the entire graph would translate two units up.

The answer is the graph stretches in the x-axis by 1/2 and translates two units up.