The differince quotient for function f(x)=mx+b

amanf

amanf

Answered question

2021-09-25

The difference quotient for the  f(x)=mx+b function

Answer & Explanation

Margot Mill

Margot Mill

Skilled2021-09-26Added 106 answers

Formula used: 
The difference quotient of the function f(x) is given by:
Difference quotient =f(x+h)f(x)h 
Calculation: 
First of all, we find an expression for f(x+h). In order to find the expression for f(x+h), we replace x by x+h in f(x). 
f(x+h)=m(x+h)+b 
f(x+h)=mx+mh+b 

We obtain the following when we enter the expressions for f(x+h) and f(x) into the difference quotient formula: 
Difference quotient =mx+mh+b(mx+b)h 
Difference quotient =mx+mh+bmxbh 
Difference quotient =mhh 
Difference quotient =m. 
Conclusion: 
On plugging the given linear function in the difference quotient formula, we get the difference quotient of the function f(x)=mx+b as m.

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