If F(x) = 3x + 4, then [F(x + h) - F(x)]/h =?

Question

is it 3 ?

Answer 1

First: replace "x+h" with the x-variable in the function...

F(x+h) = 3(x+h) + 4
F(x+h) = 3x + 3h + 4

Sec: take the result "3x + 3h + 4" and subtract the original function...

[(3x + 3h + 4) - (3x + 4)]/h

Third: solve the expression, eliminate parenthesis > distribute the negative sign with the terms in the 2nd parenthesis

[3x + 3h + 4 - 3x - 4]/h

*Combine "like" terms...

[3x - 3x + 3h + 4 - 4]/h

3h/h

Cancel "like" terms...

= 3

Answer 2

F(x) = 3x + 4

Let's do this one at a time. Before we solve the big formula, let's solve the smaller one first.

F(x + h) = 3(x + h) + 4, so
F(x + h) = 3x + 3h + 4

Now, all we have to do is plug this into our big formula.

[F(x + h) - F(x)]/h = [ [3x + 3h + 4] - [3x + 4] ] / h

First, let's distribute the minus sign.

[F(x + h) - F(x)]/h = [ 3x + 3h + 4 - 3x - 4 ] / h
[F(x + h) - F(x)]/h = [3h] / h

Cancelling out the h terms, we get 3.
You are correct.

Answer 3

F(x) = 3x + 4

so
F(x + h) = 3(x + h) + 4
F(x + h) = 3x + 3h + 4

so
[F(x + h) - F(x)]/h

= [ (3x + 3h + 4) - (3x + 4) ] / h

= [ 3x + 3h + 4 - 3x - 4 ] / h

hence we get

[F(x + h) - F(x)]/h = 3h / h

hence we get 3 after cancelling h in numerator and denomenator.

so it is CORRECT to say that

[F(x + h) - F(x)]/h = 3.

Answer 4

yes, it is
Drudge: Are you a student in Junior High or Middle School? Or are you making up the lessons to get a high school diploma?

Answer 5

Puggy did a good job. He's right.(or she?)