Functions and limits

Question 1

Rate of change

Answer 1

f(x2)-f(x1)/x2-x1
plug in x2 and subtract what you get for x1 and divide by given x2 and x1

Question 2

Graphing piece-wise functions

Answer 2

Plug in numbers for x that follow the restriction.

Question 3

Steps to simplify the difference quotient.

Answer 3

1. Plug in f(h+x) to the function
2. Plug in f(h) to the function
3. Combine the two
4. Divide by the denom.
5. Simplify as much as possible

Question 4

How do you find the limit on a graph

Answer 4

Find the x-value where the graph will approach
Look the the y-value the graph approaches for the left and right side
If they match, the limit is that number
If they don’t match the limit DNE

Question 5

How do you use a graph to find the limit

Answer 5

Look at given x you approach
Trace from left and right
If they approach the same y value, that’s the limit

Question 6

How to find the limit of an equation

Answer 6

1. Try direct substitution (if the answer is not 0 or infinity, that’s the limit)
2. If it is 0 or infinity, try to factor
3. If you can’t factor, use conjugates

Question 7

How to find the limit of a piecewise function with the neg or pos

Answer 7

If its neg., look at the function that is less than
If it’s pos., look at the function that is greater than and plug in the limit