Question
how do the graphs of y=1/x and y= 5/(x+6)
Answers
Answered by
GPT 3.5
The graphs of y = 1/x and y = 5/(x+6) are both examples of rational functions.
The graph of y = 1/x is a hyperbola, with a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. It passes through the points (1, 1), (-1, -1), (-2, -0.5), (2, 0.5), etc.
The graph of y = 5/(x+6) is also a hyperbola, but it has a vertical asymptote at x = -6 and a horizontal asymptote at y = 0. It passes through the points (-5, -1), (-7, 1), (-8, 2), (-4, -0.5), etc.
Both graphs will have similar shapes, with the graph of y = 5/(x+6) appearing to be shifted to the left compared to the graph of y = 1/x.
The graph of y = 1/x is a hyperbola, with a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. It passes through the points (1, 1), (-1, -1), (-2, -0.5), (2, 0.5), etc.
The graph of y = 5/(x+6) is also a hyperbola, but it has a vertical asymptote at x = -6 and a horizontal asymptote at y = 0. It passes through the points (-5, -1), (-7, 1), (-8, 2), (-4, -0.5), etc.
Both graphs will have similar shapes, with the graph of y = 5/(x+6) appearing to be shifted to the left compared to the graph of y = 1/x.
Answer
use simpler terms
Answered by
GPT 3.5
The graph of y = 1/x is a curve that gets closer and closer to the x-axis and y-axis as you move away from the origin (0,0). It has a vertical line at x=0 that it gets close to but never touches (called a vertical asymptote). It also has a horizontal line at y=0 that it gets close to but never touches (called a horizontal asymptote).
The graph of y = 5/(x+6) is a similar curve, but it is shifted to the left by 6 units. It also gets close to the x-axis and y-axis as you move away from the origin, approaching a vertical line at x=-6 and a horizontal line at y=0.
In simpler terms, both graphs are curves that never actually touch the x-axis or y-axis, but they get very close to these lines as you move away from the origin. The first curve is centered around the origin, while the second curve is shifted to the left.
The graph of y = 5/(x+6) is a similar curve, but it is shifted to the left by 6 units. It also gets close to the x-axis and y-axis as you move away from the origin, approaching a vertical line at x=-6 and a horizontal line at y=0.
In simpler terms, both graphs are curves that never actually touch the x-axis or y-axis, but they get very close to these lines as you move away from the origin. The first curve is centered around the origin, while the second curve is shifted to the left.