AP Calculus Summer Review

What are the steps to solving a complex fraction?

1. Find the small denominators

2. Find the LCD of those small denominators

3. Multiply the fraction by LCD/LCD

4. Distribute the LCD along top and bottom

5. Cancel out small denominators

6. Simplify what is left

What is the difference quotient?

f(x+h)-f(x)/h

How do you use the difference quotient?

1. Find f(x+h) by replacing every x in the function with x+h

2. Find f(x) by writing the original function

3. Place f(x+h) - f(x) in the num.

4. Place h in the den.

5. Simplify

How do you find the x-intercepts?

Set y=0

How do you find y-intercepts?

Set x=0

The elimination and substitution methods are used in what?

Systems

Show the interval notation for -2 < x ≤ 4

(-2, 4]

When do you use parenthesis in interval notation? Is the circle closed or open on a graph?

Less than/greater than; open circle

When do you use brackets in interval notation? Is the circle open or closed?

Less than or equal to/greater than or equal to; closed circle

How do you find the inverse of a function?

1. Rewrite f(x) as y

2. Switch x and y

3. Solve for new y

4. Simplify

5. Solve for y

6. Rewrite in inverse notation; f ^-1 (x)

How do you prove one function is an inverse of another?

Property of Inverses: f(g(x)=g(f(x))=x

Slope intercept form

y=mx+b

Vertical line (slope is undefined)

x=c

Horizontal line (slope is 0)

y=c

Point-slope form

y-y₁=m(x-x₁)

If two lines are parallel their slopes…

Are the same

If two lines are perpendicular their slopes are…

Negative reciprocals; flip it, switch the sign