The graph of y= g(x) is shown. Draw the graph of y= g(-x) + 2

Question

The original coordinates are (0,0) (-2,4) (4,2) . Transforming the graph.

Answer 1

We are given points (x, g(x)) at the values x=-2, 0, and 4 and want to graph as many points (x, g(-x)+2) as we can evaluate from knowledge of g(x). So to use all the three known values, we must have points x where the value in parentheses for g is -2, 0, and 4. Since the parentheses now have a negative sign, x must also change sign to keep the value in parentheses the same.

So we will have points where:

1) -x=-2, g(-x)+2=g(-2)+2, or in other words x=2, g(-x)+2=g(-2)+2.

2) -x=0, g(-x)+2=g(0)+2, or in other words, x=0, g(-x)+2=g(0)+2

3) -x=4, g(-x)+2=g(4)+2, or in other words, x=-4, g(-x)+2=g(4)+2

This means the same points on the graph before flipped across the line of the y axis and shifted up by 2.

Feel free to let me know if you have any questions.