## High School Functions Worksheets

**Why do We Study Math Functions?** - We know what the term “"function" generally means. But in math, a function is a relation in which no input relates to more than one output. This means that a function is a relation with one output for each input.
These functions are the bases of all mathematical operations. With functions, we learn how to solve various algebraic equations and it is the base platform for calculus. You will learn how to place them on the graph and solve equations through them. Functions teach us a lot of techniques to solve problems, alongside developing the skills to make sense of various problems and helping us to find the relevant, appropriate method in solving them. Functions also help in constructing viable arguments to support your answers. They also help in increasing concentration and help you in learning how to structure the questions that need to be solved. Functions are a very elusive concept for many students. They help us understand the world around us and are essential in the business world. Have you ever thought of buying a car or calculated how long it will take you to get to a location (while accounting for other variables); then you have come across functions before.

### Interpreting Functions

- Relations as Functions (HSF-IF.A.1) - Relations are sets that have inputs and outputs. A function is a relation that has a single output per input given.
- Domains and Ranges of Functions (HSF-IF.A.2) - Domain is a cumulative term for all the possible inputs a function has. The range is the possibility of what can come from those inputs.
- Evaluating Functions (HSF-IF.A.2) - These worksheets show students how to get comfortable with working with functions.
- Evaluating Advanced Functions (HSF-IF.A.2) - These can be a little more clunky, at first, for students.
- Variable Expressions and Sequences (HSF-IF.A.3) - Understanding all the aspects of this topic can be a bit overwhelming.
- Functions versus Relations (Solutions Included) (HSF-IF.B.5) - Students will be able to separate the two concepts here.
- Determining and Predicting the Rate of Change of Functions (HSF-IF.B.6) - This is a skill that directly applies to many forms of science.
- Graphing Linear and Quadratic Functions (HSF-IF.C.7a) - Being able to place these functions on a graph is a fundamental skill.
- Graphing Square and Cube Roots (HSF-IF.C.7b) - There is a set trend that follows each form.
- Graphing Polynomial Functions (HSF-IF.C.7c) - Start with the intercepts and then predict the symmetry that may exist.
- Graphing Rational Functions (HSF-IF.C.7d) - This is a more primitive version than you will see in advanced classes.
- Graphing Exponential and Logarithmic Functions (HSF-IF.C.7e) - We not only plot them but start to use the graphs to make predictions based on the lines.
- Classifying Even and Odd Functions (HSF-IF.C.8) - It all comes don to where they fall on the graph and symmetry.
- Expressions for Exponential Functions (HSF-IF.C.8b) - We help this topic take on other forms.
- Comparing Functions in Different Formats (HSF-IF.C.9) - We use the different formats because they make it more understandable for our audience.
- Explicit Expressions and Recursive Processes (HSF-BF.A.1a) - Students will learn how to reshape formulas and expressions.
- Exponential Decay (HSF-BF.A.1b) - We use the rate of decay to determine the end value of many practical situations.
- Composition of Functions (HSF-BF.A.1c) - We understand the concept top to bottom after this.
- Manipulating the Graphs of Functions (HSF-BF.B.3) - Learn how to use a graph to your advantage.
- Inverses of Discrete Functions (HSF-BF.B.4a) - We learn how to put them in reverse and make use of the outcome.
- Graphing The Inverse of Functions (HSF-BF.B.4c) - These can help us pull apart a function and make it more useful based on what we are faced with.
- The Inverse Relationship of Logarithms and Exponents (HSF-BF.B.5) - These polar opposites can be used to help us better understand a situation.
- Invertible Functions (HSF-BF.B.4d) - This is when a one to one relationship exists between inputs and outputs.
- Converting Between Logarithmic and Exponential Functions (HSF-BF.B.5) - These are more interchangeable then you will first realize.
- Comparing Linear and Exponential Functions (HSF-LE.A.1a) - I remember this as linear (meaning line) are straight lines and exponentials are curves.
- Constructing Linear, Quadratic, and Exponential Models of Data (HSF-LE.A.2) - This is not much of a curve ball for you at all.
- Radians, Degrees, and Arc Length (HSF-TF.A.1) - These are all fundamental measures of circle math.
- Using and Understanding the Unit Circle (HSF-TF.A.2) - It is important to note that the circle is placed at the origin (0,0) when this is examined.
- Using the Unit Circle Reference Angles (HSF-TF.A.2) - These distinct divisions of the unit circle help us make accurate predictions.
- Using the Unit Circle with Trigonometric Identities (HSF-TF.A.3) - This is when you apply right triangles to the unit circle.
- Symmetry of the Unit Circle and Odd-Even Properties (HSF-TF.A.4) - Each form of behavior is explained and examined here.
- Modeling Phenomena with Trigonometric Functions (HSF-TF.B.5) - This has huge applications in a variety of engineering calculations.
- Applying Trigonometric Identities (HSF-TF.B.5) - There is a series of rules and common occurrences that can help us learn more about a system.
- Modeling Periodic Phenomena with Trigonometric Functions (HSF-TF.B.6) - When a phenomenon occurs at a predictable interval, we have a great range of applications for it.
- Pythagorean Trigonometric Identities (HSF-TF.C.8) - As usual, right triangles make the world go around in geometry.

### Building Functions

### Linear, Quadratic, & Exponential Models

### Trigonometric Functions