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write a function that is shifted down 2 units and then reflected over the x-axis. parent function is y = -5x - 8

1.) g(x) = 3(-x)+4

2.) Vertical compression by a factor of 1/3

Step-by-step explanation:

For the first image, "let g(x) be a vertical shift of f(x) = -x up 4 units followed by a vertical stretch factor of 3."

You can stretch or compress an entire graph by multiplying the equation by a constant, C.

If C > 1, it's a stretch.

If 0 < C < 1 , it's a compression.

So anyways, C goes in front of the parent function to transform it.

With the stretch, your equation is now 3(-x)

Then just go up 4 units by adding 4 to the end of your equation,

g(x) = 3(-x)+4, and you're done :)

2.) Referring back to what I said about compressions and stretches, multiplying a constant in front of the entire equation will be a vertical transformation.

if 0 < C < 1 , it's a compression.

1/3 is greater than 0 and less than 1 so it's a compression :)

true

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