When graphing the function mc026-1.jpg on your graphing calculator, what is the most appropriate viewing wi...

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When graphing the function mc026-1.jpg on your graphing calculator, what is the most appropriate viewing window for determining the domain and range of the function?

CramX · Accepted Answer

Step 1: : To determine the most appropriate viewing window for the given function, we need to first identify the key features of the graph such as the zeros, local maximums/minimums, and asymptotes (if any).. Step 2: : Looking at the given function, we can see that it's a rational function with a vertical asymptote at x = 3 and a horizontal asymptote at y = 2.. There are no visible zeros or local maximums/minimums in the visible portion of the graph. Step 3: : To include the vertical asymptote at x = 3, we should set the left boundary of the window to be less than 3, say. x = -5. To include the horizontal asymptote at y = 2, we should set the bottom boundary of the window to be 1, since the minimum value of the function is slightly above 2. Step 4: : To determine the proper right boundary of the window, we need to find out how far the graph extends to the right.. Since there are no visible zeros or local maximums/minimums, we can estimate this by looking at the rate of change of the function. The function appears to decrease slowly as x increases, so we can set the right boundary to be a few units greater than x = 3. Step 5: : Similarly, to determine the top boundary of the window, we need to find out how far the graph extends above the horizontal asymptote.. Since the function approaches the asymptote from below, we can set the top boundary to be a few units above y = 2. Step 6: : Based on the above analysis, a good viewing window for the given function would be:. -5 leq x leq 7 quad text{and} quad 1 leq y leq 6 Final Answer: The most appropriate viewing window for determining the domain and range of the given function is (-5, 7] x [1, 6].

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QuestionMathematics

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Full Solution Locked

Step 1:
: To determine the most appropriate viewing window for the given function, we need to first identify the key features of the graph such as the zeros, local maximums/minimums, and asymptotes (if any).

Step 2:
: Looking at the given function, we can see that it's a rational function with a vertical asymptote at x = 3 and a horizontal asymptote at y = 2.

Step 3:
: To include the vertical asymptote at x = 3, we should set the left boundary of the window to be less than 3, say

Step 4:
: To determine the proper right boundary of the window, we need to find out how far the graph extends to the right.

Step 5:
: Similarly, to determine the top boundary of the window, we need to find out how far the graph extends above the horizontal asymptote.

Step 6:
: Based on the above analysis, a good viewing window for the given function would be:

Final Answer

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Full Solution Locked

Step 1:: To determine the most appropriate viewing window for the given function, we need to first identify the key features of the graph such as the zeros, local maximums/minimums, and asymptotes (if any).

Step 2:: Looking at the given function, we can see that it's a rational function with a vertical asymptote at x = 3 and a horizontal asymptote at y = 2.

Step 3:: To include the vertical asymptote at x = 3, we should set the left boundary of the window to be less than 3, say

Step 4:: To determine the proper right boundary of the window, we need to find out how far the graph extends to the right.

Step 5:: Similarly, to determine the top boundary of the window, we need to find out how far the graph extends above the horizontal asymptote.

Step 6:: Based on the above analysis, a good viewing window for the given function would be: