Students formalize the periodicity, frequency, phase shift, midline, and amplitude of a general sinusoidal function by understanding how the parameters A, w, h, and k in the formula
f(x) = Asin(w(x-h))+k

are used to transform the graph of the sine function, and how variations in these constants change the shape and position of the graph of the sine function.

Students learn the relationship among the constant A, w, h, and k in the formula f(x) = Asin(w(x-h))+k
and the properties of the sine graph.

Students review how changing the parameters A, ω, h, and k in f(x) = A sin(ω(x - h)) + k affects the graph of the sine function.
Students examine the example of the Ferris wheel, using height, distance from the ground, period, and so on, to write a function of the height of the passenger cars in terms of the sine function: f(x) = A sin(ω(x - h)) + k.

Students graph the tangent function.
Students use the unit circle to express the values of the tangent function for π - x, π + x, and 2π - x in terms of tan(x), where x is any real number in the domain of the tangent function.

Students solve simple logarithmic equations using the definition of logarithm and logarithmic properties.

Students interpret addition and multiplication of two irrational numbers in the context of logarithms and find better-and-better decimal approximations of the sum and product, respectively.
Students work with and interpret logarithms with irrational values in preparation for graphing logarithmic functions.

Students graph the functions f(x) = log(x), g(x) = log2(x), and h(x) = ln(x) by hand and identify key features of the graphs of logarithmic functions.

Students compare the graph of an exponential function to the graph of its corresponding logarithmic function.
Students note the geometric relationship between the graph of an exponential function and the graph of its corresponding logarithmic function.

Students will understand that the logarithm function base b and the exponential function base b are inverse functions.

Students study transformations of the graphs of logarithmic functions.
Students use the properties of logarithms and exponents to produce equivalent forms of exponential and logarithmic expressions. In particular, they notice that different types of transformations can produce the same graph due to these properties.

Students understand that the change of base property allows us to write every logarithm function as a vertical scaling of a natural logarithm function.
Students graph the natural logarithm function and understand its relationship to other base b logarithm functions. They apply transformations to sketch the graph of natural logarithm functions by hand.

Students analyze data and real-world situations and find a function to use as a model.
Students study properties of linear, quadratic, sinusoidal, and exponential functions.

Students use geometric sequences to model situations of exponential growth and decay.
Students write geometric sequences explicitly and recursively and translate between the two forms.

Students develop a general growth/decay rate formula in the context of compound interest.
Students compute future values of investments with continually compounding interest rates.

Students apply knowledge of exponential and logarithmic functions and transformations of functions to a contextual situation.

Students use the sum of a finite geometric series formula to develop a formula to calculate a payment plan for a car loan and use that calculation to derive the present value of an annuity formula.

Students will compare payment strategies for a decreasing credit card balance.
Students will apply the sum of a finite geometric series formula to a decreasing balance on a credit card.

Students use geometric series to calculate how much money should be saved each month to have 1 million in assets within a specified amount of time.

Students draw a smooth curve that could be used as a model for a given data distribution.
Students recognize when it is reasonable and when it is not reasonable to use a normal curve as a model for a given data distribution.

Students understand that the sum or difference of two polynomials produces another polynomial and relate polynomials to the system of integers; students add and subtract polynomials.