|
2.3 Vocabulary for Graphs of Exponential Functions |
|
|
|
|
|
Concave down |
|
If a graph turns to the right (turns “clockwise”) as you travel along the curve from left to right, the graph is concave down. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
These graphs are concave down. |
|
|
|
|
|
Concave up |
|
If a graph turns to the left (turns “counterclockwise”) as you travel along the curve from left to right, the graph is concave up. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
These graphs are concave up. |
|
|
|
|
|
|
|
Domain of a function |
|
The set of input values which yield an output value. The set of “allowable values” for the input. |
|
|
|
Exponential function |
|
A function whose output changes by a percentage amount for each unit change in the input. The rate of change, therefore is NOT constant like it is with a linear function. Exponential functions can either exhibit growth or decay. |
|
|
|
Growth (or decay) Factor |
|
The number used as the multiplier in an
exponential growth (or decay) function.
In the expression, |
|
|
|
In a growth
function, with a growth rate r, the growth factor |
|
|
|
|
|
|
|
In a decay function with a decay rate of r, the decay factor |
|
|
|
|
|
|
|
Growth (or decay) Rate |
|
The percentage of change in an exponential growth (or decay) function. |
|
|
|
In a growth function with a factor of a,
the growth rate is |
|
|
|
|
|
|
|
In a decay function with a factor of a,
the decay rate |
|
|
|
|
|
|
|
Horizontal Asymptote |
|
The horizontal line, |
|
|
|
Symbolically we write: |
|
|
|
|
|
|
|
Linear function A function with a constant rate of change. Its graph is a straight line. We call the constant rate of change the slope of the line.
Range |
|
The set of output values for a function.
The average rate of
change of a linear function, often signified by the variable, m. The slope, m =
|
|
|
|
|
