Analyzing Linear and Exponential Functions
Linear Function:
A linear function is a function that can be represented graphically in the coordinate plane by a straight line. It is a first degree polynomial which can be represented as:
f(x) = m x + c
where: m and c are constants and x is a real variable.
The constant m is called slope and m ≠ 0
c is called y-intercept.
Example of a Linear Function
f(x) = x + 10
The above function can be represented by the following graph
A linear function is a function that can be represented graphically in the coordinate plane by a straight line. It is a first degree polynomial which can be represented as:
f(x) = m x + c
where: m and c are constants and x is a real variable.
The constant m is called slope and m ≠ 0
c is called y-intercept.
Example of a Linear Function
f(x) = x + 10
The above function can be represented by the following graph
Exponential Functions:
An Exponential Function is a function which can be represented as:
y = ab ^ x
where both a and b are greater than 0 and b is not equal to 1.
Example of Exponential Function
y= 2 ^ x
The above function can be represented by the following graph
An Exponential Function is a function which can be represented as:
y = ab ^ x
where both a and b are greater than 0 and b is not equal to 1.
Example of Exponential Function
y= 2 ^ x
The above function can be represented by the following graph
Linear Function Represented Algebraically
Following is the example of a linear function represented algebraically:
f(x) = 2x – 1
Linear Function Expressed Verbally
Following is the example of a linear function expressed verbally:
The output or the function of the input is the number 3 added to twice the input.
Comparison Of The Above Two Functions
In order to compare the above two functions, let us consider the graphs of the functions.
Following is the example of a linear function represented algebraically:
f(x) = 2x – 1
Linear Function Expressed Verbally
Following is the example of a linear function expressed verbally:
The output or the function of the input is the number 3 added to twice the input.
Comparison Of The Above Two Functions
In order to compare the above two functions, let us consider the graphs of the functions.
From the above graphs it is evident that the slope of both the functions is 2. The y-intercept of the first function is (0,-1) whereas the y-intercept of the second function is (0,3). The x-intercept of the first function is (1/2,0) whereas the y-intercept of the second function is (-3/2,0). Both are same in respect that both are increasing. Also both have same end behavior of:
As x -> ∞ , y -> ∞
As x -> - ∞ , y -> - ∞
Also both the functions do not have a minimum or maximum, and both have a domain and range of:
Domain: -∞ < x < ∞
Range: -∞ < y < ∞
As x -> ∞ , y -> ∞
As x -> - ∞ , y -> - ∞
Also both the functions do not have a minimum or maximum, and both have a domain and range of:
Domain: -∞ < x < ∞
Range: -∞ < y < ∞