Grade 12 Function Relations Worksheet
A Grade 12 Math worksheet focusing on understanding and analyzing function relations, including domain, range, inverse functions, and composition of functions.
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Grade 12 Function Relations
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. Which of the following relations is NOT a function?
{(1,2), (2,3), (3,4)}
{(1,2), (1,3), (2,4)}
{(x,y) | y = x + 5}
{(x,y) | y = x²}
2. The domain of the function f(x) = 1 / (x-3) is:
x ≠ 0
x ≠ 3
x > 3
All real numbers
3. The of a function is the set of all possible output values (y-values).
4. If f(g(x)) = x and g(f(x)) = x, then f and g are functions.
5. Given the function f(x) = 2x - 5, find its inverse function, f⁻¹(x).
6. For the functions f(x) = x² + 1 and g(x) = x - 3, find (f ∘ g)(x).
7. All relations are functions.
True
False
8. The graph of an inverse function is a reflection of the original function across the line y = x.
True
False
9. Plot the relation {(−2, 4), (−1, 1), (0, 0), (1, 1), (2, 4)} on the coordinate plane. Is this relation a function? Explain your reasoning.