Question

Write an equation for a function that has a graph with the given characteristics.

Answer 1

Answer:

y = $\frac{1}{x+3}-8$

Step-by-step explanation:

When you change anything horizontally, you only change the x part. When you change anything vertically, you change the whole function.

In this case, since you shift left 3 units, you only alter the x:

y = $\frac{1}{x}$ becomes y = $\frac{1}{x+3}$

It's x + 3 instead of x - 3 because horizontal is kind of backwards. - means right and + means left.

Now, when you shift down 8, you are altering the whole function, so:

y = $\frac{1}{x+3}$ becomes y = $\frac{1}{x+3}-8$

Notice that this time, it's - 8 and not + 8 because vertical is not backwards like horizontal is: - means down and + means up.

So, the answer is y = $\frac{1}{x+3}-8$.