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.