Questions
MAT135H5_F25_ALL SECTIONS 1.4 Preparation check
Multiple choice
Read the Horizontal Line Test in the textbook Links to an external site. . Which of the following statements are equivalent to (i.e. say the same thing as) the Horizontal Line Test? Select all that apply.
Options
A.A function
𝑓
is one-to-one if and only if there is no horizontal line that intersects the graph of
𝑓
exactly once.
B.A function
𝑓
is one-to-one if and only if there is no horizontal line that intersects the graph of
𝑓
more than once.
C.A function
𝑓
is one-to-one if and only if there is no horizontal line that intersects the graph of
𝑓
twice or more.
D.A function
𝑓
is one-to-one if and only if every horizontal line intersects the graph of
𝑓
either once or not at all.
E.A function
𝑓
is one-to-one if and only if every horizontal line intersects the graph of
𝑓
at least once.
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Step-by-Step Analysis
Question restatement: The Horizontal Line Test characterization of a one-to-one function is being asked, and you need to select all statements that are equivalent to the test.
Option A: 'A function f is one-to-one if and only if there is no horizontal line that intersects the graph of f exactly once.' This is incorrect because the Horizontal Line Test allows intersections of zero or one time for each horizontal line; requiring that there be no line that intersects exactly once would exclude legitimate one-to-one functions (which can have lines that touch the graph in exactly one point). In other words, it over-restricts the condit......Login to view full explanationLog in for full answers
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