Can anyone help explain how to do #3?

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Expert Answers
justaguide eNotes educator| Certified Educator

The point (2, 3) is on the graph of y =f(x). The corresponding coordinates of this point on the graph of `y = -2*(f(2(x+5)) - 4` has to be determined.

Let the required coordinates be (x', y')

x' = 2(x+5)

=> x' = 2x + 10

Substituting x = 2, x' = 14

y' = -2*3 - 4 = -10

The coordinates of the point on the graph of `y = -2*(f(2(x+5)) - 4` that correspond to the point (2, 3) is on the graph of `y =f(x)` is (14, -10)

Zaca | Student

This is a translation problem.

We are trying to find out how the point (2, 3) would shift if it was put into the function `y=-2(f(2(x+5))-4`  

First we start with the x value. `x=2`  

What happens to the x value when we put it into the function?

It gets increased by five: `x=2+5=7`  

Then it gets multiplied by 2: `x=7*2=14`  

Since the only what happens inside of the f(x) parenthesis determines the x value, we know that the corresponding value of x is 14.

To determine y, figure out how y is transformed in the equation: (Note: `y=3`)

First it is multiplied by -2: `y=3*-2=-6`  

Then decreased by 4: `y=-6-4=-10`




Answer `(14, -10)`