Graphing functions – Grade 11 math lesson
Lesson 11 of 23 in the Grade 11 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 11 (ages 16–17) 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 11 (ages 16–17)
- 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: “How can a graph help you solve an equation you cannot solve by hand?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Joining plotted points of a curve with straight lines. Draw a smooth curve through the points.
- Mixing up the shapes of x² and x³ graphs. Try x = −2: is y positive or negative?
Tip for home: Sketch a graph of a journey to school and tell its story.
What your child will learn
Learning goal: recognize, sketch and interpret graphs of linear, quadratic, cubic and reciprocal functions.
Success looks like
- I can recognize graph shapes.
- I can read solutions from a graph.
- I can interpret real-life graphs.
Key words
- linear
- a straight-line graph
- quadratic
- a U-shaped curve
- cubic
- an S-shaped curve with x³
- reciprocal
- y = k/x, two curves that never touch the axes
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Plot y = x² and y = x³ from tables of values and compare the shapes.
The big ideas (for the adult)
Each type of function has a typical shape: straight line (linear), U or ∩ shape (quadratic), S shape (cubic) and two separate curves (reciprocal).
Read graphs to solve equations: the solutions of f(x) = k are where the graph meets the line y = k.
Real-life graphs tell a story: on a distance-time graph, steeper means faster and flat means stopped.
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 11 math lessons
- Complex numbers
- Radicals
- Vectors
- Laws of exponents
- Square roots and cube roots
- Systems of equations
- Rational expressions and polynomials
- Arithmetic and geometric sequences
- Iteration
- Functions
- Exponential functions
- Trigonometric functions
- Law of sines and law of cosines
- Coordinate geometry
- Counting outcomes
- Experimental probability
- Compound events
- Conditional probability
- Expected value
- Box plots and interquartile range
- Scatter plots and lines of fit
- Sampling and making inferences
Curriculum
Common Core State Standards HSF.BF.B.3: “Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.”
Common Core State Standards HSF.IF.C.7.c: “Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.