What a Function Really Is: Words, Tables, Formulae & Graphs (Grade 10)

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Grade 10 · Functions and Graphs

MEMORANDUM

Name:

Class:

Date:

Mark

/ 22

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Explain, in your own words, what makes a relationship a FUNCTION.
(2)
Every input has exactly ONE output ✓; no input may give two different answers ✓(2)
2
Write the rule “multiply by 3, then subtract 4” as a formula in function notation.
(2)
f(x) = 3x − 4 ✓✓(2)
3
Determine the rule for the table x: 1, 2, 3, 4 → y: 5, 8, 11, 14.
(3)
Constant difference of 3, so y = 3x + c ✓; 5 = 3(1) + c so c = 2 ✓; y = 3x + 2 ✓(3)
4
If f(x) = 4x − 7, determine f(3).
(2)
f(3) = 4(3) − 7 ✓ = 5 ✓(2)
5
If f(x) = x² + 2x, determine f(−3).
(2)
(−3)² + 2(−3) = 9 − 6 ✓ = 3 ✓(2)
6
If f(x) = 5x + 1, determine the value of x for which f(x) = 26.
(2)
5x + 1 = 26 ✓; x = 5 ✓(2)
7
Write down the domain and the range of f(x) = x².
(2)
Domain: x ∈ ℝ (all real numbers) ✓; Range: y ≥ 0 ✓(2)
8
Explain why f(x) = x² is still a function even though f(−4) and f(4) are both 16.
(2)
Two different inputs are allowed to give the same output ✓; the rule is only broken if ONE input gives two different outputs ✓(2)
9
State the vertical line test and say what it tells you.
(2)
Slide a vertical line across the graph ✓; if it ever cuts the graph more than once the graph is not a function, because that x-value has more than one y-value ✓(2)
10
A taxi charges R12 to get in plus R7 per kilometre. Write a formula for the cost C of a journey of k kilometres, and calculate the cost of a 15 km trip.
(3)
C = 7k + 12 ✓✓; C = 7(15) + 12 = R117 ✓(3)

TOTAL: 22 marks