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)
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)`