Solving Exponential Equations
This video shows examples of changing constants in graphs of functions using exponential equations.
Changing Constants in Graphs of Functions: Exponential Equations
The standard form of an exponential equation is y equals a to the x, where the x is the exponent. The constant would just be a right here.
If a is positive, like it is in these first two graphs, 2 or 1/2, then the graph of the exponential equation is above the x axis. If a is negative, like it is here in the third graph, then the graph is below the x axis.
When I say the absolute value of a is greater than 1, that would be the first and the last graphs. The absolute value of 2 and -2 is both 2. 2 is greater than 1.
When the absolute value of a is greater than 1, then as the graph moves to the right it’s approaching infinity or negative infinity. As it moves to the left it’s approaching the x axis.
You can see that the opposite is true for the middle graph. When the absolute value of a is less than 1, like one half is less than 1, or negative one half would be less than 1, than the exact opposite is true.
As the graph moves to the right it’s approaching the x axis, and as it moves to the left it’s approaching infinity or negative infinity.
The other thing we can say about a is as the absolute value of a increases, or it as a gets further away from one in either direction, like 2 or -2- the further a is from 1, then the steeper the graph is.
The closer a is to 1, then the shallower the graph is going to be. In fact, when a is 1- if this was y equals 1 to the x, it would just be a horizontal line. It would no longer be exponential.