# Graphing Exponential Functions

• anthonych414
In summary, the conversation discusses the difficulties in understanding a certain mathematical procedure and the importance of noticing key features, such as monotone increase and asymptotes. The speaker also suggests practicing with easy values and using a calculator to graph non-integer values. The person seeking help expresses gratitude for the advice and plans to practice more to improve.
anthonych414
I can't seem to understand the procedure, can anyone post any links to a useful tutorial? I took it this year and it was the only thing I didn't understand, 3 questions about it came in my maths final and I got an 82 (I got everything else right but I made a small calculation mistake in a question involving trig in space), and since I plan on taking AP calculus next year I want to understand the concept.

There's a limited amount you can do by hand. The most important part of graphing something like y = a^x (a>1) is to notice that:

1) It's monotone increasing
2) It has a horizontal asymptote at y = 0 as x approaches -inf
3) A y-intercept of y = 1
4) The graph gradually gets steeper the farther right you go.
5) The "steepness" depends on a. Larger a means that graph approaches infinity much faster

As far as wanting more detail than this, pick easy values to calculate. e.g.

y = 2^x

x y
1 2
2 4
3 8
4 16

If a is not an integer, just plug in a few values in your calculator and graph it that way.

edit: fixed bullet 3

Last edited:
Thank you for the help, I now have a better understanding of the concept and I will solve some exercises to perfect my technique.

## What is an exponential function?

An exponential function is a mathematical function in which the independent variable appears in the exponent. It is written in the form f(x) = ab^x, where a is the initial value, b is the base, and x is the exponent.

## How do you graph an exponential function?

To graph an exponential function, you need to plot several points on a coordinate plane and then connect them with a smooth curve. You can find these points by choosing different values for x and calculating the corresponding values for f(x) using the function's equation.

## What is the shape of an exponential function graph?

The graph of an exponential function has a distinctive shape, resembling a J-curve. It starts at the initial value and then quickly rises or falls, depending on the base of the function. It can also approach but never touch the x-axis.

## What are the key features of an exponential function graph?

The key features of an exponential function graph are the initial value, the y-intercept, the direction of the curve (whether it is increasing or decreasing), and the asymptote, which is the line that the graph approaches but never touches.

## How can you use a graph of an exponential function to solve real-life problems?

The graph of an exponential function can be used to model various real-life situations, such as population growth, radioactive decay, and compound interest. By analyzing the graph, you can determine the initial value, the rate of change, and the future values of the variable being modeled.

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