Question

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

Answer 1

Answer:

$(-7, -4)$

$(-4, 2)$

$(-4, 1)$

Step-by-step 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:  $(-4, 1)$