Precalculus Unit 1

Big Idea:

Identify functions and their characteristics.

Student Expectations:

Focus TEKS

P.c.2A use the composition of two functions to model and solve real-world problems;

P.c.2.B demonstrate that function composition is not always commutative;

P.c.2.C represent a given function as a composite function of two or more functions;

P.c.2.D describe symmetry of graphs of even and odd functions;

P.c.2.E determine an inverse function, when it exists, for a given function over its domain or a subset of its domain and represent the inverse using multiple representations;

P.c.2.F graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions;

P.c.2.I determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing;

P.c.2.G graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems

Student Learning Targets:

• I will determine and analyze properties of functions
• I will understand composition of functions and that they are not always commutative
• I will identify if a situation is a function, and what type of function
• I will determine an inverse function and its properties

Essential Questions:

• What defines a function?
• What are some different types of functions?
• How can functions be represented in the real world?

Extra Information:

Adopted Textbook:

District Grading Policy

Texas Gateway Online Resource Center