Question

Find an equation for the graph sketched below

Answer 1

The equation for the sketched graph is
`y = 4^x - 2`

Finding an equation for the sketched graph

From the question, we have the following parameters that can be used in our computation:

The graph

The equation for the sketched graph is represented as

`y = ab^x + c`

Where c is the asymptote

In this case, the asymptote is at x = -2

So, we have

`y = ab^x - 2`

Using the points on the graph, we have

`2 = ab^1 - 2`

`-1 = ab^0 - 2`

This gives

-1 = a - 2

Evaluate

a = 1

Recall that

`2 = ab^1 - 2`

So, we have

2 = b - 2

b = 4

So, the equation is

`y = 4^x - 2`

Hence, the equation for the sketched graph is
`y = 4^x - 2`