Question

Which absolute value function defines this graph?

Answer 1

The first one because it has a negative slope (which is -4) and h is always the opposite while k stays the same. By the way h is the 2 and k is the 3

Answer 2

A.
`f(x)=-4|x+2|+3`

Explanation:

We have been given an image of an absolute function. We are asked to find the formula for our given absolute function.

The formula of parent absolute function is
`f(x)=|x|` with vertex at (0,0)

We can see that the vertex of our given function is at
`(-2,3)`. This means that our function is shifted to left by 2 units. We can represent this information as:
`f(x)=|x--2|=|x+2|`

We can also see that our graph is reflected across x-axis, so after reflection our function would be
`f(x)=-|x+2|`

We can see that our graph is shifted upwards by 3 units, so graph after shifting would be
`f(x)=-|x+2|+3`.

Our graph is stretched vertically by a scale factor of 4, so after stretching our function would be
`f(x)=-4|x+2|+3`.

Therefore, option A is the correct choice.