When have we done each of the following, and how do we do each?

Fundamental operations with y = f(x).

Plug the coordinates of points into the form of the function and solve for the parameters.

Substitute for y and solve for t.

Substitute for t and solve for y.

Find and interpret the average rate of change of y with respect to x.

Look at the pattern of the average rates as calculated over a series of equal intervals.

Equation-solving techniques:

Add the same quantity on both sides of an equation.

Multiply both sides of an equation by the same quantity.

Take the same power of both sides of the equation.

Take the log of both sides of the equation.

Apply the same exponential function to both sides of the equation.

Facts and properties of real numbers:

a / a = 1

1 * a = a

a^1 = a

a^0 = 1

a^(-b) = 1 / (a^b)

a ( b + c ) = ab + ac

a^b * a^c = a^(b + c)

(a^b)^c = a^(bc)

If a = b and b = c then a = c

(a^p)^(1/p) = a

Real numbers: facts and properties.

y = x

y = x^2

y = x^p

y = 2^x

Using the basic functions:

Each basic function has basic points that dictate the behavior its graph.

The transformation y = A f(x-h) + k, when applied to a basic function y = f(x), moves each basic point A times further from the x axis and then shifts the resulting point k units vertically and h units in the horizontal direction.