Examples for

Common Core Math: High School Functions

Functions are tools that mathematicians use to describe and make predictions about mathematical relationships. In high school, students formalize the definition of a function in terms of domain and range and are introduced to various new types of functions including linear, quadratic, polynomial, rational, exponential, logarithmic and trigonometric functions. Students learn to represent and transform functions using equations, graphs and numerical methods. Students analyze and compare the behavior of different types of functions, noting function properties such as growth rates, intercept values, symmetries, asymptotes, discontinuities and periodicity.
Common Core Standards

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CCSS.Math.Content.HSF-IF.A.1
high school common core standard TF.B.5

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high school functions common core standards
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Interpreting Functions

Analyze function behavior using equations, graphs and numerical representations.

Determine the domain and range of a function (CCSS.Math.Content.HSF-IF.A.1):

domain and range of y = x^2 + 4x + 3
range of f(x) = 2^x - 1

Determine intervals on which a function has a given behavior (CCSS.Math.Content.HSF-IF.B.4):

where is f(x) = 3x^2 + 9x increasing?
x^2 + x - 20 < 0
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Building Functions

Construct and observe relationships between functions.

Transform the graph of a function (CCSS.Math.Content.HSF-BF.B.3):

compare x^2 and 4x^2 - 5
plot 3^x and 3^(x - 1) + 6

Compute the inverse of a function (CCSS.Math.Content.HSF-BF.B.4):

f^(-1)(x) if f(x) = 3x^2 - 1
(x + 4)/(x^2 - 16) inverse
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Linear & Exponential Models

Identify and compare scenarios that can be modeled by linear and exponential functions.

Distinguish between linear and exponential functions (CCSS.Math.Content.HSF-LE.A.1):

f(x) = 3x and g(x) = 3^x

Construct functions (CCSS.Math.Content.HSF-LE.A.2):

line with slope 5 and y-intercept 2
exponential function through (1, 3) and (2, 9)

Solve exponential equations (CCSS.Math.Content.HSF-LE.A.4):

solve 2^x = 3 over the reals
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Trigonometric Functions

Explore values and properties of trigonometric functions and their inverses.

Analyze properties of trigonometric functions (CCSS.Math.Content.HSF-TF.B.5):

period of 6 sin(x/3) - 7
maximum of 8 cos(2t) - 1

Use inverse functions to solve trigonometric equations (CCSS.Math.Content.HSF-TF.B.7):

solve sin(x) + 3 = 4 on 0 <= x < 2pi

Apply Pythagorean identities (CCSS.Math.Content.HSF-TF.C.8):

if sin(a) = 3/5, what is cos(a)?
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