C3 Exponential and Log Functions
Mrs S Richards Hawthorn High
EXPONENTIAL FUNCTIONS and GRAPHS
An exponential function is one of the form
x
yk
where k is a constant
(which is not equal to 1), and x is the variable.
In other words an exponential function is a power function.
ALL exponential functions display similar features but we will look specifically at THE
EXPONENTIAL FUNCTION
() x
f x e
Once you know the shape of an exponential graph, you can shift it vertically or
horizontally, stretch it, shrink it, reflect it, check answers with it, and most important
interpret the graph.
The function
() x
f x e
is always positive.
There is simply no value of x that will cause the value of to be negative.
What does this mean in terms of a graph? It means that the entire graph of the function
() x
f x e
is located in quadrants I and II.
Notice that the graph never crosses the x-axis. WHY?
It is because there is no value of x that will cause the value of f(x) in the formula to equal 0.
Notice that the graph crosses the y-axis at 1. WHY?
The value of x is always zero on the y-axis. Substitute 0 for x in the equation
: .
