Questions
MAT135H5_F25_ALL SECTIONS 1.4 Preparation check
Multiple dropdown selections
For each of the following functions, use the Horizontal Line Test to determine whether it is one-to-one. a) The function in graph A is [ Select ] one-to-one NOT one-to-one b) The function in graph B is [ Select ] NOT one-to-one one-to-one c) The function in graph C is [ Select ] one-to-one NOT one-to-one d) The function in graph D is [ Select ] one-to-one NOT one-to-one e) The function in graph E is [ Select ] one-to-one NOT one-to-one
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Step-by-Step Analysis
To determine if each graph is one-to-one, we apply the Horizontal Line Test: a function is one-to-one only if every horizontal line intersects its graph at most once. Now I’ll analyze each graph option in turn, noting where the test succeeds or fails.
A) Graph A: The blue curve has a small wavy bump after leaving the origin, creating a region where the same y-value can occur at two different x-values (one on the rising segment before the bump and one on the falling segment after the bump). Because a horizontal line can cross the graph twice in that region, th......Login to view full explanationLog in for full answers
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Similar Questions
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
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.
Which of the following is NOT a one-to-one function?
Which one of the following is not a one-to-one function?
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