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Resource Type
Common Core: Math
CCLS  Math: F.IF.7
 Category
 Interpreting Functions
 SubCategory
 Analyze Functions Using Different Representations
 State Standard:
 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★
54 Results

 Student Outcomes Students graph transformations of functions in the form f(x) = 1/xn.

 Student Outcomes Students graph rational functions showing intercepts, asymptotes, and end behavior.

 Student Outcomes Students identify vertical and horizontal asymptotes of rational functions.

 Student Outcomes Students describe the end behavior of rational functions.

 In Topic B, students explore composition of functions in depth and notice that a composition of a polynomial function with the function f(x) = 1/x gives functions that can be written as ratios of...

 Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascal’s Triangle to find roots...

 Student Outcomes 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.

 Topic E is a culminating series of lessons driven by MP.4, Modeling with Mathematics. Students apply what they have learned about mathematical models and exponential growth to financial literacy...

 Student Outcomes 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...

 Student Outcomes Students study transformations of the graphs of logarithmic functions. Students use the properties of logarithms and exponents to produce equivalent forms of exponential and...

 Student Outcomes 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...

 In Topic C, students graph logarithmic functions, identifying key features (FIF.4, FIF.7) and discover how the logarithmic properties are evidenced in the graphs of corresponding logarithmic...

 Student Outcomes Students interpret addition and multiplication of two irrational numbers in the context of logarithms and find betterandbetter decimal approximations of the sum and product,...

 Exponential and Logarithmic Functions In this module, students synthesize and generalize what they have learned about a variety of function families. They extend the domain of exponential functions...

 In this topic, students develop an understanding of the six basic trigonometric functions as functions of the amount of rotation of a point on the unit circle (FTF.A.1), and then translate that...

 Student Outcomes 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...

 Student Outcomes 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,...

 Student Outcomes 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...

 Students will use trigonometric functions to model periodic phenomena (FTF.B.5) by fitting sinusoidal functions to data (SID.B.6a). Students use the properties of the graphs of sinusoidal...

 Student Outcomes Students observe identities from graphs of sine and cosine basic trigonometric identities and relate those identities to periodicity, even and odd properties, intercepts, end...

 Student Outcomes Students graph the sine and cosine functions and analyze the shape of these curves. For the sine and cosine functions, students sketch graphs showing key features, which include...

 Module 2 builds on students’ previous work with units and with functions from Algebra I, and with trigonometric ratios and circles from high school Geometry. The heart of the module is the study of...

 Student Outcomes Students model a crosssection of a riverbed with a polynomial function and estimate fluid flow with their algebraic model.

 Student Outcomes Students learn to fit polynomial functions to data values.