1.4 BUILDING FUNCTIONS FROM
FUNCTIONS
By: Alaina Riedel & Lauren Evenson
“Building Blocks,
Building Functions”
g(x) = 𝒙
f(x) = 𝒙𝟑
f(x) = 2
f(x) = 𝒙𝟐 + 4
http://www.youtube.com/watch?v=9rsJF6lqxao
Combining Functions
A way of creating new functions to combine two or
more functions to create a new function.
 The most obvious way we can do this is to perform
basic algebraic operations on the two functions to
create the new one
 Add, subtract, multiply or divide functions.
 The algebra of real numbers: 4 x 5 = 20, 4 - 5 = -1
 The algebra of functions: fg, f-g, etc
Sum, Difference, Product, and Quotient
Composition of Functions
Relations and Implicitly Defined Functions
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Relation: A set of ordered pairs of real numbers
If the relation happens to relate a single value of y
to each value of x, then the relation is also a
function and its graph will pass the vertical line test
Implicitly defined function: A function that is a subset
of a relation defined by an equation in x and y
Example - Relation
Determine which of the ordered pairs (2,-5), (1,3),
and (2,1) are in the relation defined by 𝑥 2 y +
𝑦 2 = 5. Is this relation a function?
(2,-5):
(2)2 (5) + (-5)2 = 5
(1,3):
(1)2 (3) + (3)2 = 12 = 5
(2,1):
(2)2 (1) + (1)2 = 5
So, (2,-5) and (2,1) are in the relation, but (1,3) is not.
Since the equation relates two different y-values (-5
and 1) to the same x-value (2), the relation cannot be
a function.

Example - Implicitly
The graph consists of two parallel
lines, each the graph of one of the
implicitly defined functions
Alaina & Lauren Mix Up
jeopardylabs.com
/play/building-functions-from-functions2
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Materials Used
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Pre-Calculus Book
http://facultypages.morris.umn.edu/~mcquarrb/te
achingarchive/Precalculus/Lectures/BuildingFunction
fromFunctions.pdf
http://math.ucsd.edu/~wgarner/math4c/textbook/
chapter2/combfunctions.htm
Jeopardy Game: https://jeopardylabs.com/