**Difference Quotients**

Difference quotients are expressions which represent the slope of the line between two general points on the graph of a function, such as

or

.

In simplifying a difference quotient, it is important to remember that is not the same as . To find , substitute for in the expression for .

**Ex 1** Find and simplify

for .

**Sol**

.

**Ex 2** Find and simplify

for .

**Sol**

.

**Pr 1** Find and simplify

for .

**Pr 2** Find and simplify

for .

**Pr 3** Find and simplify

for .

**Pr 4** Find and simplify

for .

**Pr 5** Find and simplify

for .

**Pr 6** Find and simplify

for .

**Pr 7** Find and simplify

for .

**Pr 8** Find and simplify

for .

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