Precalculus requires a thorough understanding of functions and the language used to work with functions.
The lessons below will give you the required review.
Be sure to clickclickclick through some of the exercises in each of these lessons!
The lessons will open in a new tab/window.
Then, do the lesson on this page to practice with difference quotients, which are particularly important in calculus.
Consider a point $\,\bigl(x,f(x)\bigr)\,$ on the graph of a function $\,f\,$.
If $\,h\,$ is a small positive number, then $\,x+h\,$ lies a little to the right of $\,x\,$.
If $\,h\,$ is a small negative number, then $\,x+h\,$ lies a little to the left of $\,x\,$.
In both cases, $\,\bigl(x+h,f(x+h)\bigr)\,$ is a point on the graph of $\,f\,$, likely close to the original point $\,(x,f(x))\,$.
The slope of the line through $\,\bigl(x,f(x)\bigr)\,$ and $\,\bigl(x+h,f(x+h)\bigr)\,$ is: $$ \cssId{s13}{\text{slope}} \cssId{s14}{= \frac{\text{change in $y$}}{\text{change in $x$}}} \cssId{s15}{= \frac{f(x+h)  f(x)}{(x+h)x}} \cssId{s16}{= \frac{f(x+h)f(x)}{h}} $$

closer to the original point $\,\bigl(x,f(x)\bigr)\,$, To keep the graph uncluttered, the labels for the new (closer) points $\bigl(x+h,f(x+h)\bigr)$ are not shown. 

Recall that the result of a division problem, $\,\frac{a}{b}\,$, is called a quotient,
and the result of a subtraction problem, $\,a  b\,$, is called a difference.
The expression $\displaystyle\,\frac{f(x+h)f(x)}{h}\,$ is called a difference quotient,
because it is a quotient of differences:
On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. 
PROBLEM TYPES:
