Question

Select the correct answer Which function is represented in this graph

F(x) = |x-1| - 5
F(x) = |x-5| - 1
F(x) = |x + 5| - 1
F(x) = |x+ 1| - 5

Answer 1

`f(x)=|x+5|-1`

Explanation:

The graph depicted is moved 5 left and 1 down from the parent function.

When the graph is horizontally moved(x axis), it is inside the absolute value signs. So it cannot be
`f(x)=|x-1|-5` or
`f(x)=|x+1|-5`

You ask, why is it not
`f(x)=|x-5|-1` ? The graph is moved left by 5 after all.

Because when the graph is moved right by 5, it is |x-5| and when its moved left by 5, it is |x+5|