6

Set 14: Linear Functions (Advanced)

Explanation

Answer: A

Which linear function has a range of all real numbers?

A.

y=2x+1y = 2x + 1

✓ Correct
B.

y=5y = 5

C.

x=3x = 3

D.

None of the above

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Diagonal lines. 1. Diagonal (m0m \neq 0): Goes up and down forever. Range is (,)(-\infty, \infty). 2. Horizontal (y=5y=5): Range is just {5}\{5\}. 3. Vertical (x=3x=3): Range is (,)(-\infty, \infty) but it's not a function. Strategic Tip: Any non-horizontal linear function covers all y-values. Choice B is incorrect. Choice C is incorrect because not a function. Choice D is incorrect.

Key Steps:

The correct answer is y=2x+1y = 2x + 1

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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