题目
MAT135H5_F25_ALL SECTIONS 1.4 Preparation check
多项选择题
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.
选项
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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标准答案
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思路分析
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 explanation登录即可查看完整答案
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类似问题
Please select whether the following functions are one-to-one (meaning their inverse is also a function). 1. 𝑓 ( 𝑥 ) = 𝑥 2 + 4 𝑥 − 5 [ Select ] not one-to-one one-to-one 2. 𝑔 ( 𝑥 ) = | 4 𝑥 − 3 | [ Select ] not one-to-one one-to-one 3. 𝑚 ( 𝑥 ) = 3 𝑥 [ Select ] not one-to-one one-to-one
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Which one of the following is not a one-to-one function?
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