Graph Transformation

Question

Suppose that the graph of a given function f(x) contains the point (9, 4). What point must be on each of the following transformed graph? Please write your answer as pints (a, b) including the parentheses. Give a brief explanation of your thinking.

a.      The graph of f(x – 6) must contain the point

b.     The graph of f(x) – 5 must contain the point

c.      The graph of f(x + 2) + 7 must contain the point

Answer 1

The point (9,4) can be thought as a solution to the function.

This is f(9) = 4

We only know that f(9) = 4 so whatever is in the parenthesis must be 9.

a)

f(x-6) to make this look like f(9) just say x-6 = 9

x = 15

So when x = 15 we have f(15-6) which is just f(9) which is 4 so the point

(15,4) must be involved.

b)

Since f(9) = 4 f(x) -5 when x = 9 is

f(9) - 5 or 4 - 5

This is just -1

this is the point (9,-1)

c)

Lastly f(x+2) + 7

To make the function f(9), x must be 7

Since f(9) = 4 f(9) + 7 = 11

This is the point (7,11)