Definition: The ratio of the change in y-values over the change in x-values. The difference quotient is simply a more complex variation of the formula for slope. ~Toolingu.com
To find this slope, let's look at a graph:
So the y coordinates of A and B are the f (x) because y = f (x)
And as shown, the x coordinates for A and B are x and (x + h), respectively
Using the distance formula, the difference in the y coordinates divided by the diference in the x coordinates, you come up with:
Simplified, the equation comes to:
*This is the ratio for the Difference Quotient*
Solving the ratio:
Here is an example equation:
First, look back at the ratio for the difference quotient.
Take the first part of the ratio, put f (x + h) into the equation and do function notation.
What I mean by this is set f (x + h) equal to 4x – 3, and continue with function notation. Function notation is when you insert (x + h) into every place there is an x value. In this case, the only x value is the 4x
To...
And for the other part, you set the other part of the ratio, f (x) equal to the equation
To...
Nothing changes, because the original equation was f (x) = 4x – 3
Going back to the ratio, take the two parts and replace them with the f (x + h) and f (x)
When you simplify, you get the final answer of... 4
Caroline Stacey
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