How do you find the Domain and Range in an Exponetial graph

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vantyne14 | Middle School Teacher | (Level 1) Adjunct Educator

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For `y = 2^x`

The domain of a function are the possible x-values while the range are the possible y-values.

Since x is an exponent and the exponent can be any real number the domain is all real numbers which is written as:

D = {all real numbers}

From the graph, it looks as if x stops at -5, this is due to the fact the as x decreases, the graph gets closer and closer to the x-axis, but never intersects it and goes below the x-axis. So, this makes the graph look like it stops at -5 when in reality it has just gotten so close to the x-axis that the computer is unable to differentiate between the two.

Now, we need to find the range. The range are the y-values. Since the graph never intersects or goes below the x-axis, the y-values are not zero or negative. This makes the range, all positive real numbers. This is written as:

R = { all positive real numbers}

This graph moves upward from left to right and is called exponential growth.


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