SOLUTION: Find the difference quotient for f(x)=3x+7 The correct answer is one of the following. Which one? A) 3h B) 3/h C) 3h^2 D) 3 E) 3/h^2

Algebra ->  Equations -> SOLUTION: Find the difference quotient for f(x)=3x+7 The correct answer is one of the following. Which one? A) 3h B) 3/h C) 3h^2 D) 3 E) 3/h^2      Log On


   

Question 1198549: Find the difference quotient for f(x)=3x+7
The correct answer is one of the following. Which one?
A) 3h
B) 3/h
C) 3h^2
D) 3
E) 3/h^2
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

The given function is linear - therefore, the difference quotient is the slope of the line, which the function describes.


The slope is 3, so the difference quotient is 3 (option D).    ANSWER

Solved.



Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

The term difference quotient refers to first finding the difference of f(x+h)-f(x), then the quotient is the ratio of that over h as shown in the steps below.

f%28x%29+=+3x%2B7

f%28x%2Bh%29+=+3%28x%2Bh%29%2B7

f%28x%2Bh%29+=+3x%2B3h%2B7

f%28x%2Bh%29-f%28x%29+=+%283x%2B3h%2B7%29-%283x%2B7%29 Difference

f%28x%2Bh%29-f%28x%29+=+3x%2B3h%2B7-3x-7

f%28x%2Bh%29-f%28x%29+=+3h

%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+%283h%29%2Fh Quotient

%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+3

The idea is that h doesn't equal zero, but we slowly approach h = 0 to find the tangent slope function.
In the case of any linear equation, the tangent slope is the slope of the linear function itself.

Answer: Choice D) 3