6

Set 14: Linear Functions

Explanation

Answer: A

Which table of values represents a linear function?

A.

x: 1, 2, 3, 4; y: 5, 7, 9, 11

✓ Correct
B.

x: 1, 2, 3, 4; y: 5, 10, 20, 40

C.

x: 1, 2, 3, 4; y: 1, 4, 9, 16

D.

x: 1, 2, 3, 4; y: 5, 4, 2, -1

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Check for a constant rate of change. 1. Check A: As xx goes up by 1, yy goes up by 2 (75=2,97=2,119=27 -5=2, 9-7=2, 11-9=2). Constant rate \rightarrow Linear. 2. Check B: yy doubles (Exponential). 3. Check C: Differences are 3, 5, 7 (Quadratic). 4. Check D: Differences are -1, -2, -3 (Not constant). Strategic Tip: In a linear table, the first differences of yy are constant (for equal x-steps). Choice B is incorrect (Exponential). Choice C is incorrect (Quadratic). Choice D is incorrect.

Key Steps:

The correct answer is x: 1, 2, 3, 4; y: 5, 7, 9, 11

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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