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Someone claims that a straight-line charge might never cross the vertical axis. Is that possible for a rule that gives exactly one output for each input?
AYes, whenever the rate of change is negative
BNo, every such line crosses the vertical axis
CYes, whenever the starting amount is zero too
DNo, unless the rate of change happens to be 1
Answer & Solution
Correct answer: B. No, every such line crosses the vertical axis
1. The vertical axis is the place where the input is zero.
2. A rule that gives one output for each input must give some output when the input is zero.
3. That output is the point where the line meets the vertical axis, so the crossing always exists.
4. A negative rate only tilts the line downwards and does not stop it reaching the axis, so option A fails.
_Source: OpenStax College Algebra (CC BY 4.0), Ch 4 "Linear Functions", section 4.1 Linear Functions_
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