Grade 11 Functions Worksheets
Free printable functions practice for Grade 11 students. Generate problems, solve them on screen or paper, and download as PDF.
Practice Worksheet
Grade 11 Functions Practice
Solve each problem. Show your work.
- 1.State the domain of f(x) = √(x - 3) + 2: _____
- 2.Find the inverse of f(x) = 2x + 3: _____
- 3.Let f(x) = x² and g(x) = x + 2. Find (f ∘ g)(2): _____
- 4.State the domain of f(x) = √(x - 7) + 2: _____
- 5.Find the inverse of f(x) = 3x + 3: _____
- 6.Let f(x) = x² and g(x) = x + 3. Find (f ∘ g)(2): _____
Show answer key
- Question 1: x ≥ 3
- Question 2: f⁻¹(x) = (x - 3)/2
- Question 3: 16
- Question 4: x ≥ 7
- Question 5: f⁻¹(x) = (x - 3)/3
- Question 6: 25
Free Practice Worksheets
Print, solve on paper, then upload a photo for AI feedback and feedback.
Build confidence with approachable problems
Solve each problem. Take your time.
- 1.Given f(x) = 2x - 5, find f(4).
- 2.State the domain and range of the function f(x) = x² + 3.
- 3.Find the inverse function f^-1(x) for f(x) = x - 7.
- 4.Find the zeros of the quadratic function f(x) = x² - 9.
- 5.Identify the transformation of f(x) = x² that results in g(x) = x² - 4.
- 6.Find the maximum or minimum value of the quadratic function f(x) = x² + 5.
A selection of topic skills
Solve each problem. Show your work.
- 1.Given f(x) = 3x - 5, find the inverse function f^-1(x) and determine the domain and range of both f(x) and f^-1(x).
- 2.Find the zeros of the quadratic function f(x) = x² - 6x + 8 by factoring. Then, identify the coordinates of the vertex.
- 3.Describe the transformations required to obtain the graph of g(x) = -2(x + 3)² + 4 from the parent function f(x) = x².
- 4.A ball is thrown into the air such that its height h in meters after t seconds is given by h(t) = -5t² + 20t + 1. Determine the maximum height reached by the ball and the time at which it occurs.
- 5.A population of bacteria doubles every hour. If the initial population is 500, write a function P(t) to represent the population after t hours. If the laboratory needs to study the bacteria when the population reaches 8,000, how many hours will pass?
- 6.Compare the range of f(x) = |x| - 4 and g(x) = -(x²) + 5. Which function has a larger maximum value, and what is that value?
Practise specific Functions skills
Skill map
How functions skills connect
Shore up what feeds in, work through the core skills in order, then move on to what they unlock. A means the skill has an instant answer checker.
What Your Child Will Learn
Grade 11 functions formalizes function notation and asks students to think about relationships more abstractly than in previous years. Students learn to determine domain and range from equations, graphs, and real-world contexts, evaluate functions using f(x) notation, and perform operations on functions including composition and finding inverse functions algebraically and graphically.
Quadratic functions are revisited with more depth, including solving quadratic inequalities, working with the discriminant to characterize roots, and analyzing transformations more formally as mappings of points. Students also study rational and radical functions at an introductory level, identifying restrictions on the domain caused by division by zero or negative values under a square root.
Throughout the course, students are expected to move fluidly between algebraic, graphical, numerical, and verbal representations of the same function — a flexibility that becomes essential in the exponential, sequences, and trigonometric strands that follow within the same course. This unit essentially teaches students to think about math in terms of functions rather than isolated equations, a shift that underpins all subsequent senior-level math.
Skills Covered
- Evaluating and interpreting function notation f(x)
- Determining domain and range from equations and graphs
- Finding and verifying inverse functions
- Composing two functions and simplifying the result
- Solving quadratic inequalities
- Identifying restrictions on rational and radical functions
Curriculum Aligned: Foundational strand of Grade 11 Functions (MCR3U, with related content in the college-prep MCF3M), establishing function concepts used throughout senior math.
Parent Tip: Function notation like f(x) can look like a foreign language even to parents who were comfortable with algebra — it helps to remember it's just relabelled 'y'. Asking your teen to translate a line of f(x) notation into a plain-English sentence ('this means: plug 3 into the function and see what comes out') is a good comprehension check you can do without touching the math yourself.
What your child will practice
- Zeros of QuadraticsDetermine the zeros of a quadratic function using various methods.
- Function NotationRepresent functions using function notation and evaluate functions for given values.
- Domain and RangeDetermine the domain and range of functions using algebraic and graphical methods.
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Check my workFrequently Asked Questions
How often should my child practice functions?
Short daily practice sessions of 10-15 minutes are more effective than long weekly sessions. Consistency builds lasting understanding.
How do I know if my child is at the right level for these worksheets?
If your child can complete about 70% of the problems correctly, the level is appropriate. If it's too easy or too hard, try an adjacent grade level.
Can I use these worksheets for homeschool?
Yes. The worksheets align with standard curriculum expectations and can supplement any math program. Generate multiple worksheets to create a full practice set.