**Pre-Calculus Transformations**

1.7.1 Exercises

Suppose (2,?3) is on the graph of y = f(x). In Exercises 1 - 18, use Theorem 1.7 to find a point on the graph of the given transformed function.

Solve & show work : y=2f(1-x)-1

Theorem 1.7. Transformations.

Suppose f is a function. If A 6= 0 and B 6= 0, then to graph

g(x) = Af(Bx + H) + K

1. Subtract H from each of the x-coordinates of the points on the graph of f. This results in

a horizontal shift to the left if H > 0 or right if H < 0.

2. Divide the x-coordinates of the points on the graph obtained in Step 1 by B. This results

in a horizontal scaling, but may also include a re

ection about the y-axis if B < 0.

3. Multiply the y-coordinates of the points on the graph obtained in Step 2 by A. This results

in a vertical scaling, but may also include a re

ection about the x-axis if A < 0.

4. Add K to each of the y-coordinates of the points on the graph obtained in Step 3. This

results in a vertical shift up if K > 0 or down if K < 0.

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