The graph of y=h(x) is shown. Draw the graph of y= 2h(x)-3

Question

The original coordinates are (0,0) (2,4) (4,0)

Its quite confusing.

Answer 1

So, we have a vertical stretch of 2 and it's moved down 3. What does that look like?

The simple way is to remember that h(x) means what is y for the given x. When x = 0, h(0) = 0, so we have your first point of (0,0).

So, the x's won't change but your y will.

If we take the same x = 0 with the original y (aka f(0)) and put it into the new equation.

2(0) - 3 = -3, so our first new point is (0,-3)

The new f(2) = 2(4) - 3, etc

Go.

Answer 2

I deleted my previous answer as I was mis-interpreting the new function definition. Yes, the 'x' value stays the same, it just gets processed once for h(x) and then again to compute the new function value.