What transformations change the graph of (f)x to the graph of g(x)?

f(x) = -7x² ; g(x) = -35x²+5

stretch vertically by 5:

-35x^2

shift up 5:
-35x^2 + 5

Thank you

so the +5 number would always be up

and a -5 number would always be down?

The answer is D: the graph of g(x) is the graph of f(x) stretched vertically by a factor of 5 and translated up 5 units.

the answers are all 7s and 9s

Well, it seems like g(x) likes to party a little more than f(x). To transform f(x) into g(x), we'll need to apply some changes. Let's see what g(x) is up to:

1. The coefficient of x² in f(x) is -7, but in g(x), it's -35. Looks like g(x) is multiplying the whole thing by 5! Maybe g(x) has some serious ups and downs.

2. And wait, there's more! While f(x) is content with only -7x², g(x) is feeling extra fancy and adds a little something on top. It's got that extra 5 hanging out there at the end. Maybe g(x) just wanted to make sure it stands out in the crowd.

So, to transform f(x) into g(x), it looks like we need to multiply the whole graph by 5 and then add 5 to the end, just like g(x) does. That should do the trick! Now f(x) can join g(x) in the party. Cheers!

To determine the transformations that change the graph of (f)x to the graph of g(x), we need to compare the two equations and identify any changes in coefficients and constants. Let's break it down:

1. Vertical stretching/compression: The coefficient in front of x² determines the vertical stretching or compression. In this case, f(x) has a coefficient of -7, and g(x) has a coefficient of -35. Since -35 is greater than -7, the graph is vertically compressed.

2. Vertical translation: The constant term at the end of the equation determines the vertical translation. In f(x), there is no constant term, so the graph is not shifted up or down. In g(x), there is a constant term of +5, which shifts the graph upward by 5 units.

Therefore, the transformations applied to f(x) to get g(x) are a vertical compression and a vertical translation upwards.

Summary:
f(x) = -7x²
g(x) = -35x² + 5

Transformations:
1. Vertical compression: The graph is vertically compressed due to the coefficient of x² being greater in g(x) than in f(x).
2. Vertical translation: The graph is shifted upward by 5 units due to the constant term in g(x).

yes, because the +y axis is up