Which table represents a linear function?

If function is given by its table representation and you have to determine what type of function it is, you can’t be 100% sure that the given function is linear. Why is that so? Because there are many functions which have the same table representation.

Example: You’re given f(0)=0 and f(1)=1. It can be representation of function f(x)=x, f(x)=x^2, f(x)=x^3 etc. If there are more given datas, maybe you can eliminate some types of functions, but you can’t be sure what type of function it is. :)

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Dennis Wainaina, Student

Answered June 16, 2017

a linear function is used to relate to relate an independent variable and a dependent variable by introducing a rate of change(function) of which the independent variable is equated to find the dependent variable for example y=3x hence hence is the dependent variable as it depends on the change of x and 3 is the rate of change which is a constant and is determined by the division of the values of y/x hence to make a table of y over x of which y is determined by the rate of change 3*the independent variable x

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Clyde Maiden

Answered September 17, 2018

Line AB contains points A(4, 5) and B(9, 7). What is the slope of



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What do you meant by a function is linear?

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!