Examples for

Common Core Math: High School Functions: Building Functions

In high school, students gain familiarity with the concept of functions and learn to transform and combine functions in new ways. In particular, students learn to create new functions by transforming a given function via a dilation or translation or by composing one function with another. Students also learn the concept of inverse functions and practice computing inverses of functions when they exist.
Common Core Standards

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CCSS.Math.Content.HSF-BF.A.1
common core standard building functions B4

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common core standards about building functions
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Model with Functions

Create functions to model mathematical relationships.

Compute quantities using relationships in real-world scenarios (CCSS.Math.Content.HSF-BF.A.1):

fuel cost 50 miles, 20 mpg, $2.09/gal
distance traveled for 100 minutes at 4 mph
20 lb turkey frying time
$1000 loan at 7% interest for 3 years
what's a car's safe braking distance at 60 mph?

Find a function that describes terms in a sequence (CCSS.Math.Content.HSF-BF.A.2):

4, 7, 10, 13, 16, 19, ...
3, 5, 9, 17, ...
5, 14, 23, 32, 41, ...
2, 5, 10, 17, 26, 37, ...
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Transformations of Functions

Translate, dilate and flip graphs of functions by altering their equations.

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

plot y = 5x vs y = 5x + 3
compare x^2 and 4x^2 - 5
graph x^2 and -(x + 1)^2
plot 3^x and 3^(x - 1) + 6
plot cos(x) and -3cos(4x + 2) - 8

Explore properties of functions by transforming their graphs (CCSS.Math.Content.HSF-BF.B.3):

plot y = x and y = -x
compare x^2 and (-x)^2
sin(x) and sin(-x)
cos(x) and cos(x + 2Pi)
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Inverse Functions

Find inverse functions and explore their properties.

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

inverse of x^3
inverse function of log_2(x)
f^(-1)(x) if f(x) = 3x^2 - 1
(x + 4)/(x^2 - 16) inverse
inverse function calculator

Use inverse functions to solve equations (CCSS.Math.Content.HSF-BF.B.5):

x^2 = 11 solve for x
solve log2(x) = 4 over reals
solve sin(x^2 + 1) = 1/2 over [0, pi/2]
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