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

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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(52779)   (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)   (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.







Difference





Quotient



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
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