# How do you graph, find any intercepts, domain and range of #f(x)=4(1/2)^(x-1)-3#?

##### 1 Answer

Read below.

#### Explanation:

Let's think...

To find the domain, we ask ourselves...

What values of

We see that any real number will make the function be valid.

Therefore, the domain is all real numbers.

Similarly, we ask ourselves,

What is the largest and the smallest possible values you could obtain as the

Well, as

Essentially, we are heading towards -3 without ever reaching it.

Now, as

Therefore, the range is

To find the intercepts, we note the following:

On the y-intercept, the x value is 0.

On the x-intercept, the y value is 0.

Therefore, on the y-intercept, we have:

=>

=>

The y-intercept is at

Similarly, on the x-intercept, we have:

=>

=>

=>

=>

=>

=>

The x-intercept is at

As to graphing it, I recommend plugging in