The general form of an exponential function is y = bn, where b > 0 and b ≠ 1 and n is a real number.
Example:
Draw the graph of y = 3x for –1 ≤ x ≤ 2.
Solution:
x |
–1 |
–0.5 |
0 |
0.5 |
1 |
1.5 |
2 |
y |
0.33 |
0.58 |
1 |
1.73 |
3 |
5.2 |
9 |
From the graph above, we notice the following characteristics or properties of the exponential graph (curve) y = bn, where b > 0 and b ≠ 1 and n is a real number:
a) As the value of x increases, the value of y increases far more than the increase of value of x.
b) The range (or values of y) are positve real numbers (never zero).
c) The graph is asymptotic to the x-axis that is it gets very close to the x-axis but does not touch it or cross it.
d) The graph always crosses the y-axis at (0, 1)
This video gives the properties of exponential functions (where b >1). This video gives the properties of exponential functions (where 0 < b <1). Use transformations to graph an exponential functionRotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
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