Analyzing Linear and Exponential Functions
Linear Function
f(x)= 8x +9
f(x)= 8x +9
The graph above has a positive slope of 8 making the line move in an upward direction. The function states a y-intercept of 9, meaning that the line passes the y-axis at (0,9).
Exponential Function
f(x)= 9^x
f(x)= 9^x
Like normal exponential functions, this graph has a y-intercept of (0,1), because when you plug in 0 for x in an exponential function you will always get 1. This graph moves at a constant positive ratio of 9 which causes the curved line in the graph.
Linear Functions
-algebraically f(x)= 3x+10
-verbally f evaluated at x equals negative three x minus ten.
Compare
In the function expressed algebraically, it has a positive slope of three creating a line that moves upward on the graph. The function expressed verbally has a negative slope of three that moves downward on the graph. The y-intercept of first function is 10, meaning the line will cross the y-axis at (0,10). On the other hand, the y-intercept of the second function has a y-intercept of -10, meaning the line will cross the y-axis at (0,-10).
-algebraically f(x)= 3x+10
-verbally f evaluated at x equals negative three x minus ten.
Compare
In the function expressed algebraically, it has a positive slope of three creating a line that moves upward on the graph. The function expressed verbally has a negative slope of three that moves downward on the graph. The y-intercept of first function is 10, meaning the line will cross the y-axis at (0,10). On the other hand, the y-intercept of the second function has a y-intercept of -10, meaning the line will cross the y-axis at (0,-10).