Question

The graph of g(x) = |x – h| + k is shown on the coordinate grid. What must be true about the signs of h and k?

Both h and k must be positive.
Both h and k must be negative.
The sign of h must be positive, and the sign of k must be negative.
The sign of h must be negative, and the sign of k must be positive.

Answer 1

D.The sign of h must be negative and the signal of k must be positive *it’s for sure the answer

Answer 2

For this case we have:

The main function is:

`y = f (x) = | x |`

To move the graph vertically we have:

`y = f (x) + k`

If
`k> 0`, the graph moves k units up

To move the graph horizontally we have:

`y = f (x + h)`

IF
`h> 0`, the graph moves h units to the left

For this case, we want to move the graph k units up and h units counterclockwise. We have then, the following equation:

`g (x) = | x - h | + k`

Therefore, according to the definitions:

`k> 0`

`h<0`

Answer:

`k> 0`

`h<0`

Option: The sign of h must be negative, and the sign of k must be positive.