Questions: Choose the function whose graph is given below. A. y=cot x B. y=csc x C. y=tan x D. y=sec x

Transcript text: 4.5.3 Quiz: Graphs of Other Functions Question 1 of 10 Choose the function whose graph is given below. A. $y=\cot x$ B. $y=\csc x$ C. $y=\tan x$ D. $y=\sec x$

Solution

Solution Steps

Step 1: Identify the given graph

The graph shows a periodic function with vertical asymptotes and repeating U-shaped curves.

Step 2: Compare with known trigonometric functions

y = cot x: This function has vertical asymptotes and crosses the x-axis, but the graph does not match the given one.
y = csc x: This function has vertical asymptotes and repeating U-shaped curves, but the curves are not symmetric about the x-axis.
y = tan x: This function has vertical asymptotes and crosses the x-axis, but the graph does not match the given one.
y = sec x: This function has vertical asymptotes and repeating U-shaped curves symmetric about the x-axis.

Step 3: Match the graph to the correct function

The given graph matches the characteristics of the secant function, $ y = \sec x $, which has vertical asymptotes and repeating U-shaped curves symmetric about the x-axis.

Final Answer

The function whose graph is given is: D. $ y = \sec x $

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