This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

- Welcome
- Learning Math Strategies (Online)Toggle Dropdown
- Study Skills for MathToggle Dropdown
- Business MathToggle Dropdown
- Place Value in Decimal Number Systems
- Arithmetic Operations
- Basic Laws
- Operations on Signed numbers
- Order of Operations
- Some Useful Basic Numeracy
- Decimals
- Fractions
- Percents
- Ratios and Proportions
- Exponents
- Statistics
- Factoring
- Rearranging Formulas
- Solving Linear Equations
- Solving Systems of Linear Equations
- Trade and Cash Discounts
- Multiple Rates of Discount
- Payment Terms and Cash Discounts
- Markup
- Markdown
- Simple Interest
- Equivalent Values
- Compound Interest
- Equivalent Values in Compound Interest
- Nominal and Effective Interest Rates
- Annuities

- Hospitality MathToggle Dropdown
- Place Value in Decimal Number Systems
- Arithmetic Operations
- Order of Operations
- Basic Laws
- Prime Factorisation and Least Common Multiple
- Fractions
- Decimals
- Percents
- Exponents
- Units of Measures
- Fluid Ounces and Ounces
- Metric Measures
- Yield Percent
- Recipe Size Conversion
- Ingredient Ratios
- Food-Service Industry Costs

- Engineering Math
- Basic Laws
- Operations with Numbers
- Prime Factorisation and Least Common Multiple
- Fractions
- Exponents
- Reducing Radicals
- Factoring
- Rearranging Formulas
- Solving Linear Equations
- Areas and Volumes of Figures
- Congruence and Similarity
- Functions
- Domain and Range of Functions
- Basics of Graphing
- Transformations
- Graphing Linear Functions
- Graphing Quadratic Functions
- Solving Systems of Linear Equations
- Solving Quadratic Equations
- Solving Higher Degree Equations
- Trigonometry
- Graphing Trigonometric Functions
- Graphing Circles and Ellipses
- Exponential and Logarithmic Functions
- Complex Numbers
- Number Bases in Computer Arithmetic
- Linear Algebra
- Calculus
- Set Theory
- Modular Numbers and Cryptography
- Statistics
- Problem Solving Strategies

- Upgrading / Pre-HealthToggle Dropdown
- Basic Laws
- Place Value in Decimal Number Systems
- Decimals
- Significant Digits
- Prime Factorisation and Least Common Multiple
- Fractions
- Percents
- Ratios and Proportions
- Exponents
- Reducing Radicals
- Metric Conversions
- Factoring
- Solving Linear Equations1
- Solving Quadratic Equations
- Polynomial Long Division
- Exponential and Logarithmic Functions
- Statistics

- Nursing MathToggle Dropdown
- Arithmetic Operations
- Order of Operations
- Place Value in Decimal Number Systems
- Decimals
- Fractions
- Percents
- Ratios and Proportions
- Interpreting Drug Orders
- Oral Dosages
- Dosage Based on Size of the Patient
- Parenteral Dosages
- Intravenous (IV) Administration
- Infusion Rates for Intravenous Piggyback (IVPB) Bag
- General Dosage Rounding Rules

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You can think of a function like a machine. You input something into the machine and the function will output something.

For example, the function may be a machine that triples every number.

Another example may be the function \(x^2 +1\). This function takes every input and squares it, then adds it by 1.

A function can be named anything, the most common function names are \(f\) and \(g\). There is an input inside the function that can also be denoted by any letter, but most commonly it is denoted by \(x\). Thus, \[f(x)\]

means that the name of the function is \(f\) and the **input** is \(x\). The output is what it is equal to.

\[f(x)=x^2\]

is read "*f of x equals x squared*" where \(x^2\) is the **output**.

Another example \[g(A)=A+2\]

is a function that is named \(g\), with **input** \(A\), and the **output **adds all inputs by 2 to get \(A+2\).

There are special functions with a specific names for example \(sin(x)\) and \(ln(x)\).

All possible values (or elements) that can be inputted into a function belong to what we call the **domain**. Whereas all possible elements that can be outputted belong to what we call the **range **or **codomain**.

Not every equation can be a function, a function must have the following:

- every element in the
**domain**has a unique output in the range (called the one-to-one property) - no input is left out (called the onto property)

In other words, one element cannot lead to two outputs in the range.

This is a function because every element in the domain X has one unique output, and every element in domain X is used. No input is left out.

This is not a function because the element 2 in the domain has more than one output and not every element in the domain is used (e.g., 3 and 4 have no outputs).

For \(f(x) = 2x^2 -1\), \(g(y) = 9y +3\), \(h(x) = \sqrt{2x-1}\), find

- \(f(3) \)
- \(g(-3) \)
- \(h(A) \)
- \(f(x+1) \)
- \(g(y^2) \)
- \(h(9x+3) \)

\(f(3) \) means that for the function named \(f\), which is represents \(2x^2 -1\), the input is 3 or \(x=3\). In other words, substitute \(x=3\) into \(2x^2 -1\) and find the output.

\(f(3) = 2(\textbf{3})^2 -1 = 2(\textbf{9}) - 1 = 17\)

\(g(-3) \) means to substitute \(y=-3\) into \(g(x) = 9y +3\)

\(g(-3) = 9(\textbf{-3}) +3 = 30\)

\(h(A) \) means to substitute \(x=A\) into \(h(x) = \sqrt{2x-1}\)

\(h(A) = \sqrt{2A-1}\)

\(f(x+1) \) means to substitute \(x=x+1\) into \(f(x) = 2x^2-1\)

\(f(x+1) =2(\textbf{x+1})^2-1\)

\(g(y^2) \) means to substitute \(y=y^2\) into \(g(y) = 9y +3\)

\(g(y^2) = 9(\textbf{y^2}) +3\)

\(h(9x+3) \) means to substitute \(x=9x+3\) into \(h(x) = \sqrt{2x-1}\)

\(h(A) = \sqrt{2(\textbf{9x+3})-1} = \sqrt{\textbf{18x+6}-1} = \sqrt{18x+5}\)

Designed by Matthew Cheung. This work is licensed under a Creative Commons Attribution 4.0 International License.

- Last Updated: Mar 27, 2023 5:08 PM
- URL: https://libraryguides.centennialcollege.ca/mathhelp
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