Functions – Grade 10 math lesson
Lesson 4 of 16 in the Grade 10 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 10 (ages 15–16) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 10 (ages 15–16)
- You need
- Paper, a pencil and this page
- Graded
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Why must a function give only one output for each input?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Doing composite functions in the wrong order. fg(x): the function next to x (g) goes first.
- Thinking f⁻¹(x) means 1/f(x). The inverse undoes the function; it is not a reciprocal.
Tip for home: Think of real "functions": a vending machine gives one item for each code.
What your child will learn
Learning goal: use function notation, composite functions and inverse functions.
Success looks like
- I can use function notation.
- I can find composite functions.
- I can find inverse functions.
Key words
- function
- a rule giving one output for each input
- input
- the value put in
- composite function
- one function applied after another
- inverse function
- the function that undoes it
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Play "function machine": one person picks a secret rule, others give inputs and guess the rule.
The big ideas (for the adult)
A function gives exactly one output for each input. f(x) = 3x + 1 means "multiply by 3 and add 1": f(4) = 13.
A composite function does one function then another: fg(x) means do g first, then f.
An inverse function undoes the function: if f(x) = 3x + 1, then f⁻¹(x) = (x − 1)/3.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.
More practice
More Grade 10 math lessons
- Factoring
- Quadratic equations
- Identities and proof
- Graphing functions
- Exponential functions
- Circles: circumference and area
- Volume and surface area
- The Pythagorean theorem
- Right triangle trigonometry
- Transformations
- Similarity and congruence
- Properties of quadrilaterals
- Coordinate geometry
- Cross sections of 3-D figures
- Geometric constructions
Curriculum
Common Core State Standards HSF.BF.A.1.b: “Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.”
Common Core State Standards HSF.BF.B.4.a: “Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x³ or f(x) = (x+1)/(x-1) for x ≠ 1.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.