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marissa [1.9K]
3 years ago
14

I just need the answer to this, you don't need to show your work :)

Mathematics
1 answer:
daser333 [38]3 years ago
4 0

Answer:   g(x) = -\frac{4}{x+5}+4

===========================================================

Explanation:

We start with y = 1/x

Vertically stretching it by a factor of 4 gets us to y = 4/x. Simply multiply the right hand side by 4.

Then reflecting over the y axis means we replace every x with -x to get y = 4/(-x) but that simplifies to y = -4/x. So we can see that any y axis reflection is identical to an x axis reflection, and vice versa. This is due to the symmetry of hyperbolas like this.

Next, we replace x with (x+5) so that we shift the xy axis 5 units to the right, giving the illusion the curve shifts 5 units to the left.

Lastly, we tack on a +4 to shift the graph up 4 units.

The final result is g(x) = -\frac{4}{x+5}+4

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