Function Operations – Practice Problems
Having fun while studying, practice your skills by solving these exercises!
- Video
- Practice Problems
A function is a particular kind of relation between sets. A function takes every element x in a starting set, called the domain, and tells us how to assign it to exactly one element y in an ending set, called the range. Often functions are written in a form like f(x)=3x+5, where x is the element in the domain and 3x+5 gives the y which x is “sent to” in the range.
Functions can be combined using arithmetic operations which are similar to those used on polynomials: always combine like terms, remember the FOIL method, and don’t forget to simplify if the answer can be simplified! Here are some examples of performing operations with the functions f(x) = x² – 2x + 1 and g(x) = x – 1:
Add: f(x) + g(x)
(f + g)(x) = f(x) + g(x)
= (x² – 2x + 1) + (x – 1)
= x² – 2x + x + 1 – 1
= x² – x
Subtract: f(x) – g(x)
(f – g)(x) = f(x) – g(x)
= (x² – 2x + 1) – (x – 1)
= x² – 2x – x + 1 + 1
= x² – 3x + 2
Multiply: f(x) ∙ g(x)
(f ∙ g)(x) = f(x) ∙ g(x)
= (x² – 2x + 1) (x + 1)
= x³ – 2x² + x² + x – 2x + 1
= x³ – x² – x + 1
Divide: f(x) ÷ g(x)
(f ÷ g)(x) = f(x) ÷ g(x)
= (x² – 2x + 1) ÷ (x – 1)
= [(x – 1)(x – 1)] ÷ (x – 1)
= x – 1
We need to perform operations on functions to calculate the change of temperature, compare production rates of companies, create phone apps, and so much more.
This lesson is also a prerequisite for studying composite functions.
Build a function that models a relationship between two quantities.
CCSS.MATH.CONTENT.HSF.BF.A.1.B
Determine the total cost of the sand-proof glass carpet dome. |
Establish the equation to calculate Jaanav total profit. |
Examine the total cost of the production with Janaav's brother's new glass dome machine. |
Figure out the price for one dome. |
Decide what the correct rules are for combining functions. |
Calculate each operation with the given functions. |