Exponential Function

[happysmiler07]

Hello I am in the final two weeks of an online College Algebra class. Unfortunately, our textbook does not really explain concepts well and I am stuck with the question of how do I even approach this?

As the base of a function f(x) = a^x for a > 1 increases, what happens to the behavior of the graph for x > 0 and happens to the behavior of the graph for
x < 0? You can sketch a graph.

So here is what I have figured out so far: If 0 < b < 1 , the function decays as x increases.
If b > 1 , the function grows as x increases. 1. The exponential function with base b is defined by F(x)=B^x where b is >0, b=1 where x is any real numbers.

How do I go about making an equation that answers this?

 

[Quaid]

I am stuck with the question of how do I even approach this?

Hi happysmiler:

Pick some specific values for the base, and graph the resulting functions. (Google will graph these, for you. Simply enter y=5^x into the search field, for example.)

Graphs are pictures of function behavior, so the pictures will help you answer the questions.

As the base of a function f(x) = a^x for a > 1 increases, what happens to the behavior of the graph for x > 0 and [what] happens to the behavior of the graph for x < 0?

So here is what I have figured out so far: If 0 < b < 1 , the function decays as x increases.

This is true, but the question specifically states that the bases are greater than one.

(Do you intend symbol b to represent 'the base' above? I ask because a symbol is already given for the base; it's a, not b.

Pick some values for a that are bigger than 1, such as 2, 8, 16. Plot the graphs, and see what happens to the curve, as the base gets bigger.

If b > 1 , the function grows as x increases. 1. The exponential function with base b is defined by F(x)=B^x where b is >0, b=1 where x is any real numbers.

How do I go about making an equation that answers this?

Is this a second exercise? (See green highlighting.)

I'm not sure what this question is. The part highlighted in blue above represents two different situations. Is the question a two-part question? (1 is greater than zero.)

Also, do not switch back-and-forth between upper- and lower-case symbols because b is a different symbol than B, just as function name f is different from function name F.

Please clarify your post.

Let us know, if you have difficulty describing what you see happening.

Cheers