Question
Describe how the graph of g (x) = 3/x-4 + 5 is a translation of g (x) =3/x
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Answer
Describe how the graph of g (x) = 3/x-4 + 5 is a translation of g (x) = 3/x
A It is a translation of g (x) = 3/x, 4 units left and 5 units up
B It is a translation of g (x) = 3/x, 4 units right and 5 units up
C It is a translation of g (x) = 3/x, 4 units left and 5 units down
D It is a translation of g (x) = 3/x, 4 units right and 5 units down
A It is a translation of g (x) = 3/x, 4 units left and 5 units up
B It is a translation of g (x) = 3/x, 4 units right and 5 units up
C It is a translation of g (x) = 3/x, 4 units left and 5 units down
D It is a translation of g (x) = 3/x, 4 units right and 5 units down
Answered by
GPT 3.5
The graph of g(x) = 3/x is a hyperbola with the vertical asymptote x = 0 and the horizontal asymptote y = 0. It opens upward in the first and third quadrants and downward in the second and fourth quadrants.
To describe how the graph of g(x) = 3/(x-4) + 5 is a translation of g(x) = 3/x, we need to analyze the effects of the translation.
1. Horizontal Translation:
The expression (x-4) in the denominator of g(x) = 3/(x-4) shifts the graph 4 units to the right. Therefore, the new vertical asymptote will be x = 4, and the graph will have a gap on the left of the vertical asymptote.
2. Vertical Translation:
The addition of 5 at the end of the expression g(x) = 3/(x-4) + 5 translates the whole graph 5 units upward. This means all the points of the graph move vertically upward by 5 units.
Combining these effects, the translated graph of g(x) = 3/(x-4) + 5 will have its vertical asymptote at x = 4, a gap on the left side, and all the points will be shifted 5 units above their original positions on the graph of g(x) = 3/x.
To describe how the graph of g(x) = 3/(x-4) + 5 is a translation of g(x) = 3/x, we need to analyze the effects of the translation.
1. Horizontal Translation:
The expression (x-4) in the denominator of g(x) = 3/(x-4) shifts the graph 4 units to the right. Therefore, the new vertical asymptote will be x = 4, and the graph will have a gap on the left of the vertical asymptote.
2. Vertical Translation:
The addition of 5 at the end of the expression g(x) = 3/(x-4) + 5 translates the whole graph 5 units upward. This means all the points of the graph move vertically upward by 5 units.
Combining these effects, the translated graph of g(x) = 3/(x-4) + 5 will have its vertical asymptote at x = 4, a gap on the left side, and all the points will be shifted 5 units above their original positions on the graph of g(x) = 3/x.
Answered by
GPT 3.5
The correct answer is A) It is a translation of g (x) = 3/x, 4 units left and 5 units up.
As described in the previous answer, the expression (x-4) in the denominator shifts the graph 4 units to the right. Therefore, it is a translation of 4 units to the left relative to the graph of g(x) = 3/x.
Additionally, the addition of 5 at the end of the expression g(x) = 3/(x-4) + 5 translates the whole graph 5 units upward. Therefore, it is a translation of 5 units up relative to the graph of g(x) = 3/x.
As described in the previous answer, the expression (x-4) in the denominator shifts the graph 4 units to the right. Therefore, it is a translation of 4 units to the left relative to the graph of g(x) = 3/x.
Additionally, the addition of 5 at the end of the expression g(x) = 3/(x-4) + 5 translates the whole graph 5 units upward. Therefore, it is a translation of 5 units up relative to the graph of g(x) = 3/x.
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