GRAPHS IMPORTANT

Question

The graph of y=f(x)= is given below on the left and the graph of y=g(x)is given on the right. Find a formula for g based on transformations of the graph of f. Check your answer by confirming that the points shown on the graph of g satisfy the equation y=g(x).

(when answering pls label the variables (1,2,3.. or a,b,c...) when writing the answers, THANK YOU)

Answer 1

Note that there are 4 labelled points plus (0, 0) on the left side and 5 labelled points on the right side. That actually makes everything easy. The slope at (-3, -1) of g(x) being undefined being mapped from (0, 0) confirms the reasonableness of this procedure.

g(x) =c f(x--3) - 1 = c f(x+3) - 1

We only need to find c.

Note that we have (-2, -3)

Then, as we had (1, 1) before,

g(-2) = c f(-2+3) - 1 = c f(1) - 1 = c * 1 - 1 = c - 1

-3 = c - 1

-2 = c

g(x) = -2 f(x+3) - 1 = -2 (x+3)^1/3 - 1

To check

g(-11) = -2 (x+3)^1/3 - 1 = -2 (-11+3)^1/3 - 1 = -2 (-8)^1/3 - 1 = -2 * -2 - 1 = 3

g(-4) = -2 (x+3)^1/3 - 1 = -2 (-4+3)^1/3 - 1 = -2 (-1)^1/3 - 1 = -2 * -1 - 1 = 1

g(-3) = -2 (x+3)^1/3 - 1 = -2 (-3+3)^1/3 - 1 = -2 (0)^1/3 - 1 = -2 * 0 - 1 = -1

g(-2) = -2 (x+3)^1/3 - 1 = -2 (-2+3)^1/3 - 1 = -2 (1)^1/3 - 1 = -2 * 1 - 1 = -3

g(5) = -2 (x+3)^1/3 - 1 = -2 (5+3)^1/3 - 1 = -2 (8)^1/3 - 1 = -2 * 2 - 1 = -5