Which of the following rational functions is graphed below?
2 answers:
Answer:
The graphed rational function corresponds to:
Option: B
B.
Detailed explanation:
Examining the graph indicates vertical asymptotes at x=1 and x= -1.
- The vertical asymptotes occur where the denominator equals zero.
- If the numerator’s degree is lower than the denominator’s, y=0 acts as the horizontal asymptote.
Only function B meets both criteria:
B.
(For option A, denominator zeros are at x=0 and -1, so vertical asymptotes lie there.
Option C has vertical asymptotes at x=0 and 1.
Option D has a single vertical asymptote at x=0, which doesn’t match the graph.)
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If the point (4,-1) is part of the graph of y = f(x), then the related point on the graph of y = g(x) would be: (4,-1/2), (2,-1), (-1,-1), (1,4), (4,-4), (-12,1)
=> (4,-1/2)
=> (2,-1)
=> (-1,-1)
=> (1,4)
=> (4,-4)
=> (-12,1)
Further explanation
- Dividing the function by 2 results in all the y-values being halved as well. Thus, to determine the new point, we take the y-value (-1) and halve it to arrive at -1/2. Hence, the new point is (4,-1/2).
- When 2 is subtracted from the function's input, it shifts all x-values up by 2. Therefore, to adjust the x-value (4), we add 2 to get 2. Thus, the new point is (2,-1).
- Making the function's input negative alters each x-value by multiplying by -1. Consequently, to find the new point, we take x-value (4) and apply -1 to get -1. Therefore, the new point is (-1,-1).
- Multiplying the function's input by 4 results in each x-value being divided by 4. To find the new x-value from 4, we divide by 4 to get 1. Hence, the new point becomes (1,4).
- When multiplying the entire function by 4, each y-value is increased fourfold. Thus, the original value of 4 becomes -4, making the new point (4,-4).
- By multiplying the entire function by -1, each y-value is also multiplied by -1. As a result, the new y-value becomes 1, leading to the new point (-12,1).
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Answer details
Grade: 9
Subject: mathematics
Chapter: corresponding point
Keywords: corresponding point, the graph, point on the graph