Question

(-6,1) is a point on the graph of y=g(x)

What point is on the graph of y=g(x+1)-5?


What point is on the graph of y= -2g(x-2)+4?


What point is on the graph of y=g(2x+2)?

Answer in an ordered pair

Answer 1

`(-7, -4)`

`(-4, 2)`

`(-4, 1)`

Explanation:

We know that the point (-6, 1) belongs to the main function g(x)

The transformation

`y = g (x + 1) -5`

add 1 to the input variable (x) and subtract 5 to the output variable (y)

So the point in the graph of
`y = g (x + 1) -5` is

`x + 1 =-6\\x = -7`

`y= 1-5\\y = -4`

The point is:
`(-7, -4)`

The transformation

`y = -2g(x -2) +4`

subtract two units from the input variable (x), multiply the output variable (y) by -2 and then add 4 units

So the point in the graph of
`y = -2g(x -2) +4` is

`x -2 =-6\\x = -4\\\\y = -2(1)+4\\y = 2`

The point is:
`(-4, 2)`

The transformation

`y=g(2x+2)`

Multiply the input variable (x) by 2 and then add two units

So the point in the graph of
`y=g(2x+2)` is

`2x +2 =-6\\2x = -8\\x=-4`

`y=1`

The point is:
`(-4, 1)`