Question

3. The function f(x) has the coordinates below. State the changes made to f(x) which result in the function g(x). Write the (x,y) rule that would transform the coordinates of f(x) to the coordinates of g(x). g(x) = -2f(x + 1) - 4

Answer 1

Problem

The function f(x) has the coordinates below. State the changes made to f(x) which result in the function g(x). Write the (x,y) rule that would transform the coordinates of f(x) to the coordinates of g(x). g(x) = -2f(x + 1) - 4

Solution

From this table we know that

f(-1) = 5, f(2) = 1, f(6)=0

The rule for this case would be:

y= 13/84x^2 -125/84x +47/14

We also know that we have the following transformation

g(x) = -2f(x + 1) - 4

The corresponding coordinates of x on g(x) are:

0, 3, 7

So we have this:

f(0) = 47/14

f(3)= 2/7

f(7) = 11/21

And the corresponding y coordinates are:

-2(47/14) -4=-75/7

-2(2/7) -4=-3277

-2(11/21) -4=-106/21