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)

Answer 1

Hi Babe - great question! I like this one because they give you actually number values for the coordinates (rather than just a drawing or a formula), so you can really see what's happening with the graph.

The easiest way I could think to draw the new graph is to literally re-write the points according to the formula given. Let's use a table to see what's happening here. Since we're told y=h(x), we can re-write each point in a table as follows:

Point x y (or h(x)) 2h(x)-3 (or 2y-3) Transformed point

(0,0) 0 0 2*0 - 3 = -3 (0,-3)

(2,4) 2 4 2*4 - 3 = 8-3 = 5 (2,5)

(4,0) 4 0 2*0 - 3 = -3 (4,-3)

Notice how the "transformed point" at the end uses the same x values as the original point, and the y value of the "transformed point" just takes the original y values, multiplies them by 2, and subtracts 3.

So the transformed graph is (0,-3), (2,5) (4,-3).

Hope this helps!