Graph of Exponential Parent Function
The graph of the exponential parent function, also known as the standard exponential function, can be written as:
f(x) = a^x
where “a” is a positive constant greater than 1
The graph of the exponential parent function, also known as the standard exponential function, can be written as:
f(x) = a^x
where “a” is a positive constant greater than 1.
To create the graph, we can start with a simple example using a = 2. Let’s plot a few points to get started:
For x = -3, f(-3) = 2^(-3) = 1/8. So, we have the point (-3, 1/8).
For x = -2, f(-2) = 2^(-2) = 1/4. So, we have the point (-2, 1/4).
For x = -1, f(-1) = 2^(-1) = 1/2. So, we have the point (-1, 1/2).
For x = 0, f(0) = 2^0 = 1. So, we have the point (0, 1).
For x = 1, f(1) = 2^1 = 2. So, we have the point (1, 2).
For x = 2, f(2) = 2^2 = 4. So, we have the point (2, 4).
For x = 3, f(3) = 2^3 = 8. So, we have the point (3, 8).
Now, let’s plot these points on a graph:
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-3 -2 -1 0 1 2 3
This is a basic exponential graph of the parent function y = 2^x. As x increases, the y-values increase rapidly. Visually, the shape of the graph is a curve that starts near the y-axis and moves upward to the right.
Remember, the above graph is for the parent function with a = 2. If you want to graph other exponential parent functions, you can use the same process, adjusting the value of “a”. The larger the value of “a”, the steeper the curve will be.
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