How to graph inverse variation - Geometry
Card 1 of 36
Give the 
-intercept of the graph of the equation 
.
Give the
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Set 
in the equation:
The 
-intercept is 
.
Set
The
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Give the 
-intercept(s), if any, of the graph of the equation
Give the
Tap to reveal answer
Set 
in the equation and solve for 
.
This is impossible, so the equation has no solution. Therefore, the graph has no 
-intercept.
Set
This is impossible, so the equation has no solution. Therefore, the graph has no
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Give the vertical asymptote of the graph of the equation
Give the vertical asymptote of the graph of the equation
Tap to reveal answer
The vertical asymptote is 
, where 
is found by setting the denominator equal to 0 and solving for 
:
This is the equation of the vertical asymptote.
The vertical asymptote is
This is the equation of the vertical asymptote.
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Give the -intercept(s), if any, of the graph of the equation
Give the
Tap to reveal answer
Set in the equation and solve for .
The 
-intercept is 
Set
The
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Give the horizontal asymptote, if there is one, of the graph of the equation
Give the horizontal asymptote, if there is one, of the graph of the equation
Tap to reveal answer
To find the horizontal asymptote, we can divide both numerator and denominator in the right expression by 
:
As 
approaches positive or negative infinity, 
and 
both approach 0. Therefore, 
approaches 
, making the horizontal asymptote the line of the equation 
.
To find the horizontal asymptote, we can divide both numerator and denominator in the right expression by
As
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Electrical power can be generated by wind, and the magnitude of power will depend on the wind speed. A wind speed of 
(in 
) will generate a power of 
. What is the minimum wind speed needed in order to power a device that requires 
?
Electrical power can be generated by wind, and the magnitude of power will depend on the wind speed. A wind speed of
Tap to reveal answer
The simplest way to solve this problem is to plug all of the answer choices into the provided equation, and see which one results in a power of 
.
Alternatively, one could set up the equation,
and factor, use the quadratic equation, or graph this on a calculator to find the root.
If we were to factor we would look for factors of c that when added together give us the value in b when we are in the form,
.
In our case 
. So we need factors of 
that when added together give us 
.
Thus the following factoring would solve this problem.
Then set each binomial equal to zero and solve for v.
Since we can't have a negative power our answer is 
.
The simplest way to solve this problem is to plug all of the answer choices into the provided equation, and see which one results in a power of
Alternatively, one could set up the equation,
If we were to factor we would look for factors of c that when added together give us the value in b when we are in the form,
In our case
Thus the following factoring would solve this problem.
Then set each binomial equal to zero and solve for v.
Since we can't have a negative power our answer is
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Compared to the graph 
, the graph 
has been shifted:
Compared to the graph
Tap to reveal answer
The 
inside the argument has the effect of shifting the graph 
units to the left. This can be easily seen by graphing both the original and modified functions on a graphing calculator.
The
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If you look at 
and 
on the same graph. What is the transformation that took place from 
?
If you look at
Tap to reveal answer
The graph shifts ten units to the right. The number inside the parentheses shows where and how many units the graph will shift. If it is in the parentheses with the x-coordinate, then it will shift either to the left or right. If the number is negative, it goes to the right. If it is positive, it will shift to the left.
If the number was with the y-coordinate then the graph would shift up and down.
The graph shifts ten units to the right. The number inside the parentheses shows where and how many units the graph will shift. If it is in the parentheses with the x-coordinate, then it will shift either to the left or right. If the number is negative, it goes to the right. If it is positive, it will shift to the left.
If the number was with the y-coordinate then the graph would shift up and down.
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A triangle is made up of the following points:
What are the points of the inverse triangle?
A triangle is made up of the following points:
What are the points of the inverse triangle?
Tap to reveal answer
The inverse of a function has all the same points as the original function, except the x values and y values are reversed. The same rule applies to polygons such as triangles.
The inverse of a function has all the same points as the original function, except the x values and y values are reversed. The same rule applies to polygons such as triangles.
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Give the -intercept of the graph of the equation .
Give the
Tap to reveal answer
Set in the equation:
The -intercept is .
Set
The
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Give the -intercept(s), if any, of the graph of the equation
Give the
Tap to reveal answer
Set in the equation and solve for .
This is impossible, so the equation has no solution. Therefore, the graph has no -intercept.
Set
This is impossible, so the equation has no solution. Therefore, the graph has no
← Didn't Know|Knew It →
Give the vertical asymptote of the graph of the equation
Give the vertical asymptote of the graph of the equation
Tap to reveal answer
The vertical asymptote is , where is found by setting the denominator equal to 0 and solving for :
This is the equation of the vertical asymptote.
The vertical asymptote is
This is the equation of the vertical asymptote.
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Give the -intercept(s), if any, of the graph of the equation
Give the
Tap to reveal answer
Set in the equation and solve for .
The -intercept is
Set
The
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Give the horizontal asymptote, if there is one, of the graph of the equation
Give the horizontal asymptote, if there is one, of the graph of the equation
Tap to reveal answer
To find the horizontal asymptote, we can divide both numerator and denominator in the right expression by :
As approaches positive or negative infinity, and both approach 0. Therefore, approaches , making the horizontal asymptote the line of the equation .
To find the horizontal asymptote, we can divide both numerator and denominator in the right expression by
As
← Didn't Know|Knew It →
Electrical power can be generated by wind, and the magnitude of power will depend on the wind speed. A wind speed of (in ) will generate a power of . What is the minimum wind speed needed in order to power a device that requires ?
Electrical power can be generated by wind, and the magnitude of power will depend on the wind speed. A wind speed of
Tap to reveal answer
The simplest way to solve this problem is to plug all of the answer choices into the provided equation, and see which one results in a power of .
Alternatively, one could set up the equation,
and factor, use the quadratic equation, or graph this on a calculator to find the root.
If we were to factor we would look for factors of c that when added together give us the value in b when we are in the form,
.
In our case . So we need factors of that when added together give us .
Thus the following factoring would solve this problem.
Then set each binomial equal to zero and solve for v.
Since we can't have a negative power our answer is .
The simplest way to solve this problem is to plug all of the answer choices into the provided equation, and see which one results in a power of
Alternatively, one could set up the equation,
If we were to factor we would look for factors of c that when added together give us the value in b when we are in the form,
In our case
Thus the following factoring would solve this problem.
Then set each binomial equal to zero and solve for v.
Since we can't have a negative power our answer is
← Didn't Know|Knew It →
Compared to the graph , the graph has been shifted:
Compared to the graph
Tap to reveal answer
The inside the argument has the effect of shifting the graph units to the left. This can be easily seen by graphing both the original and modified functions on a graphing calculator.
The
← Didn't Know|Knew It →
If you look at and on the same graph. What is the transformation that took place from ?
If you look at
Tap to reveal answer
The graph shifts ten units to the right. The number inside the parentheses shows where and how many units the graph will shift. If it is in the parentheses with the x-coordinate, then it will shift either to the left or right. If the number is negative, it goes to the right. If it is positive, it will shift to the left.
If the number was with the y-coordinate then the graph would shift up and down.
The graph shifts ten units to the right. The number inside the parentheses shows where and how many units the graph will shift. If it is in the parentheses with the x-coordinate, then it will shift either to the left or right. If the number is negative, it goes to the right. If it is positive, it will shift to the left.
If the number was with the y-coordinate then the graph would shift up and down.
← Didn't Know|Knew It →
A triangle is made up of the following points:
What are the points of the inverse triangle?
A triangle is made up of the following points:
What are the points of the inverse triangle?
Tap to reveal answer
The inverse of a function has all the same points as the original function, except the x values and y values are reversed. The same rule applies to polygons such as triangles.
The inverse of a function has all the same points as the original function, except the x values and y values are reversed. The same rule applies to polygons such as triangles.
← Didn't Know|Knew It →
Give the -intercept of the graph of the equation .
Give the
Tap to reveal answer
Set in the equation:
The -intercept is .
Set
The
← Didn't Know|Knew It →
Give the -intercept(s), if any, of the graph of the equation
Give the
Tap to reveal answer
Set in the equation and solve for .
This is impossible, so the equation has no solution. Therefore, the graph has no -intercept.
Set
This is impossible, so the equation has no solution. Therefore, the graph has no
← Didn't Know|Knew It →