1. How do the graphs of y=1/x and y=5/(x+6) compare?
I need steps because I want to be able to do these type of problems. Thank you!
You should have an idea what y = 1/x looks like,
y = 1/(x+6) simply shifts the y = 1/x six units to the left.
the 5 instead of the 1 means that the y value is 5 times as great, so it rises faster or there is a vertical stretch by a factor of 5
e.g. the point (1,1) on y = 1/x becomes (1, -1/7) after y = 1/(x+6) and then (1, -5/7) under y = 5/(x+6)
here is a picture:
http://www.wolframalpha.com/input/?i=plot+y%3D1%2Fx+and+y%3D5%2F(x%2B6)
To compare the graphs of y=1/x and y=5/(x+6), follow these steps:
Step 1: Analyze the equations
The equation y=1/x represents a hyperbola, while y=5/(x+6) is a transformed version of the hyperbola.
Step 2: Determine the vertical and horizontal asymptotes
For y=1/x, the vertical asymptote is x=0, and the hyperbola does not touch or intersect this line. The graph approaches but does not cross the x-axis.
For y=5/(x+6), the vertical asymptote is x=-6, and the graph also approaches but does not cross it.
Step 3: Find the x and y-intercepts
For y=1/x, the graph intersects the y-axis at (0, 1) and does not intersect the x-axis.
For y=5/(x+6), the graph intersects the y-axis at (0, 5), and it does not intersect the x-axis.
Step 4: Plot additional points
To obtain additional points, select x-values and plug them into the equation to determine the corresponding y-values.
Step 5: Use a graphing tool or software
Plot the points obtained from Step 3 and Step 4 on a graphing tool or software. Connect the points smoothly to form the graph.
Step 6: Analyze the graph
Examine the graph to identify any transformations, such as vertical and horizontal shifts. Compare the shapes and locations of the two graphs.
By following these steps, you can compare the graphs of y=1/x and y=5/(x+6) and analyze their similarities and differences.
To compare the graphs of y = 1/x and y = 5/(x+6), you can follow these steps:
Step 1: Determine the intercepts (if any):
- For y = 1/x:
- x-intercept: Set y = 0 and solve for x. In this case, since there is a fraction, we cannot have a denominator equal to zero. Therefore, there are no x-intercepts.
- y-intercept: Set x = 0 and solve for y. In this case, when x = 0, y = undefined or approaches infinity.
- For y = 5/(x+6):
- x-intercept: Set y = 0 and solve for x. In this case, we have 5/(x+6) = 0. Solving for x, we get x = -6. So the x-intercept is -6.
- y-intercept: Set x = 0 and solve for y. In this case, when x = 0, y = 5/6. So the y-intercept is 5/6.
Step 2: Determine the behavior of the graphs as x approaches positive and negative infinity:
- For y = 1/x: As x approaches positive infinity, y approaches zero, and as x approaches negative infinity, y also approaches zero. The graph has two asymptotes: x = 0 (vertical asymptote) and y = 0 (horizontal asymptote).
- For y = 5/(x+6): As x approaches positive infinity, y approaches zero, and as x approaches negative infinity, y also approaches zero. The graph also has two asymptotes: x = -6 (vertical asymptote) and y = 0 (horizontal asymptote).
Step 3: Sketch the graphs:
- Plot the intercepts: For y = 1/x, there is no x-intercept, and the y-intercept is undefined or approaches infinity (x = 0, y = undefined).
- Plot the x-intercept (-6, 0) and the y-intercept (0, 5/6) for y = 5/(x+6).
- Draw asymptotes: For y = 1/x, draw a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. For y = 5/(x+6), draw a vertical asymptote at x = -6 and a horizontal asymptote at y = 0.
- Connect the points smoothly, considering the behavior around the asymptotes. The graph of y = 1/x will approach the asymptotes but will never touch or cross them. The same applies to the graph of y = 5/(x+6).
By following these steps, you should be able to compare the graphs of y = 1/x and y = 5/(x+6).
question 1 find the y intercept of 7
y=a/(x-k) +k
7=a/(x-k) +k
7=a/(0-(-2))+5
7-5=2
2=a/2
a=4
y=4/x+2 +5
question 2-
explain the variables and what variation
60/20=3 39/13=3 27/9=3 9/3=3
direct varation y=3x
question 3-
compare graphs
shifted to the left by 6 and streched vertical by 5
question 4-
jane is organizing a fundraiser to by a ping-pong table
t=table c=shares n=new people t=500 v=n+5 v=overall people
500=(20)+v 500/20=25 n=25-5=20
20 new people
quiz 1 answers (minus graph answers *use a graphing calulator)
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