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 hand k must be positive

Answer 1

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

Answer 2

Without an image of the coordinate plane the question is referencing, I cannot answer your question, but I can tell you what it means for both k and h to be positive: the line will hit the x-axis on the right side of the origin if k is positive, and the y axis above the origin if h is positive. There may be different possibilities for h and k if both are present in an equation though so you will have to find an answer using these rules:

1. If h is a positive number (disregarding the negative sign in (x - h)) then the line will be shifted however many digits h is to the right. For example, the linear equation f(x) = (x - (+5)) + k will be shifted 5 units to the right on top of the vertical shift done by k.

2. If k is a positive number then the function will be shifted upwards by however many units k is. For example, the equation l(x) = (x - h) + 4 has a vertical shift of +4.