AP Calc AB Summer Review

Linear Function

y = x

Standard Form of a Linear Function

Ax + By = C

Point-Slope Form of a Linear Function

y - y1 = m(x - x1)

Slope-Intercept Form of a Linear Function

y = mx + b

Slope

m = (y2 - y1) / (x2 - x1)

Slope of Horizontal Line

m = 0

Slope of Vertical Line

m = undefined

Slope of Parallel Lines

m1 = m2

Slope of Perpendicular Lines

m1 = -1/m2

Quadratic Function

y = x²

Standard Form of a Quadratic Function

ax² + bx + c = 0

Vertex Form of a Quadratic Function

y = a(x - h)² + k

Axis of Symmetry Equation

x = -b/2a

Cubic Function

y = x³

Absolute Value Function

y = |x|

Square Root Function

y = sqrt(x)

Rational Function

y = p(x) / q(x)

Exponential Function

y = ab^x

Logarithmic Function

y = a log(x)

Symmetric to the y-axis

(x,y) = (-x,y)

Symmetric to the x-axis

(x,y) = (x,-y)

Symmetric to the origin

(x,y) = (-x,-y)

Even Functions

f(x) = f(-x)

Odd Functions

f(-x) = -f(x)

Domain

All possible x values

Range

All possible y values

Vertical Line Test

If you can draw a vertical line that intersects with two points of a graph, then it is not a function.

Leading Coefficient Test

If the leading coefficient of a polynomial is even, then the ends will go in the same direction. If it is odd, then it will go in opposite directions.

If it is positive, then the graph will trend upward. If it is negative, then the graph will trend downward.

Long Division of Polynomials

1. Multiply the leading term of the divisor so that the exponent is the same as the dividend’s leading term’s exponent

2. Subtract from the dividend

3. Rinse and repeat, numbers that you multiply to the divisor add to make the quotient

Synthetic Division

1. Can only be used if the divisor is a linear factor (x - k)

2. Because it’s (x-k), if -k is being added then k is negative, if -k is positive, then k is negative

3. Essentially, flip the sign that it seems to be

4. Write the coefficients of the dividend in the top row

5. Skip the first add down

6. Multiply the result by k, put the product to the diagonal slot

7. Add down

8. Repeat until there are no more slots

9. Bottom row is the coefficients of the quotient, last one is the remainder