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Advanced Geometry : How to graph inverse variation

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Example Questions

Example Question #1 : How To Graph Inverse Variation

Give the vertical asymptote of the graph of the equation

$y = \frac{2x-1}{3x+ 5}$

Possible Answers:

$x= -\frac{3}{5}$

$x = \frac{1}{2}$

$x= \frac{2}{3}$

$x= -\frac{5}{3}$

x = 2

Correct answer:

$x= -\frac{5}{3}$

Explanation:

The vertical asymptote is x = a , where is found by setting the denominator equal to 0 and solving for :

3x+ 5 = 0

3x+ 5 - 5 = 0 - 5

3x = - 5

$3x \div 3 = - 5 \div 3$

$x= -\frac{5}{3}$

This is the equation of the vertical asymptote.

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Example Question #2 : Graphing Inverse Variation

Give the -intercept(s), if any, of the graph of the equation

$y = \frac{4}{2x+ 5}$

Possible Answers:

(4,0)

$\left ( \frac{4}{5},0 \right )$

$\left ( - \frac{5}{2},0 \right )$

The graph has no -intercept.

$\left ( \frac{5}{2},0 \right )$

Correct answer:

The graph has no -intercept.

Explanation:

Set y = 0 in the equation and solve for .

$y = \frac{4}{2x+ 5}$

$\frac{4}{2x+ 5} = 0$

$\frac{4}{2x+ 5} \cdot (2x+5) = 0 \cdot (2x+5)$

4 = 0

This is impossible, so the equation has no solution. Therefore, the graph has no -intercept.

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Example Question #3 : Graphing Inverse Variation

Give the -intercept(s), if any, of the graph of the equation

$y = \frac{2x-7}{3x+5}$

Possible Answers:

$\left ( - \frac{7}{5}, 0 \right )$

$\left ( - \frac {5}{3}, 0 \right )$

The graph has no -intercept.

$\left ( \frac {2}{3}, 0 \right )$

$\left ( \frac{7}{2}, 0 \right )$

Correct answer:

$\left ( \frac{7}{2}, 0 \right )$

Explanation:

Set y = 0 in the equation and solve for .

$y = \frac{2x-7}{3x+5}$

$0 = \frac{2x-7}{3x+5}$

$0 = \frac{2x-7}{3x+5} \cdot (3x+5)$

2x-7 = 0

2x-7+ 7 = 0 + 7

2x = 7

$2x \div 2 = 7 \div 2$

$x = \frac{7}{2}$

The -intercept is $\left ( \frac{7}{2}, 0 \right )$

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Example Question #4 : Graphing Inverse Variation

Give the horizontal asymptote, if there is one, of the graph of the equation

$y = \frac{2x-7}{3x+5}$

Possible Answers:

$y = \frac{7 }{2 }$

$y = - \frac{5 }{3 }$

$y = \frac{2 }{3 }$

The graph of the equation has no horizontal asymptote.

$y = - \frac{7 }{5 }$

Correct answer:

$y = \frac{2 }{3 }$

Explanation:

To find the horizontal asymptote, we can divide both numerator and denominator in the right expression by :

$y = \frac{2x-7}{3x+5}$

$y = \frac{\frac{2x-7}{x}}{\frac{3x+5}{x}}$

$y = \frac{2- \frac{7}{x}}{3+ \frac{5}{x}}$

As approaches positive or negative infinity, $\frac{7}{x}$ and $\frac{5}{x}$ both approach 0. Therefore, approaches $\frac{2 }{3 }$ , making the horizontal asymptote the line of the equation $y = \frac{2 }{3 }$ .

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Example Question #2 : How To Graph Inverse Variation

Give the -intercept of the graph of the equation $y = \frac{4}{2x+ 5}$ .

Possible Answers:

$\left ( 0, - \frac{5}{2} \right )$

(0,4)

$\left ( 0, \frac{5}{2} \right )$

The graph has no -intercept.

$\left (0, \frac{4}{5} \right )$

Correct answer:

$\left (0, \frac{4}{5} \right )$

Explanation:

Set x= 0 in the equation:

$y = \frac{4}{2x+ 5}$

$y = \frac{4}{2 \cdot 0+ 5} = \frac{4}{ 5}$

The -intercept is $\left (0, \frac{4}{5} \right )$ .

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Example Question #191 : Algebra

A triangle is made up of the following points:

$\left \{ (2,0), (-3,5), (0,4) \right \}$

What are the points of the inverse triangle?

Possible Answers:

$\left \{ (-2,0), (3,-5), (0,-4) \right \}$

$\left \{ (0,-2), (-5,3), (-4,0) \right \}$

$\left \{ (0,2), (5,-3), (4,0) \right \}$

$\left \{ (-2,0), (-3,-5), (0,-4) \right \}$

$\left \{ (2,0), (3,5), (0,4) \right \}$

Correct answer:

$\left \{ (0,2), (5,-3), (4,0) \right \}$

Explanation:

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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Example Question #1 : How To Graph Inverse Variation

Electrical power can be generated by wind, and the magnitude of power will depend on the wind speed. A wind speed of (in $\tiny m/s$ ) will generate a power of $v^{2}+4v$ watts . What is the minimum wind speed needed in order to power a device that requires watts ?

Possible Answers:

3 m/s

8 m/s

9 m/s

6 m/s

5 m/s

Correct answer:

8 m/s

Explanation:

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 watts .

Alternatively, one could set up the equation,

$v{^2}+4v-96=0$ 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,

ax^2+bx+c .

In our case a=1, b=4, c=-96 . So we need factors of that when added together give us .

Thus the following factoring would solve this problem.

(v+12)(v-8)=0

Then set each binomial equal to zero and solve for v.

$v+12=0 \rightarrow v=-12$

$v-8=0 \rightarrow v=8$

Since we can't have a negative power our answer is {}8 m/s .

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Example Question #1 : How To Graph Inverse Variation

Compared to the graph $y=x^{2}-5$ , the graph $y=(x+4)^{2}-5$ has been shifted:

Possible Answers:

units to the right.

units down.

units to the left.

units up.

Correct answer:

units to the left.

Explanation:

The (+4) 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.

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Example Question #1 : How To Graph Inverse Variation

If you look at y=x^2+10 and $y_{1}=(x-10)^2+10$ on the same graph. What is the transformation that took place from $y\rightarrow y_{1}$ ?

Possible Answers:

100 units to the right

units to the right

units up

units to the left

units down

Correct answer:

units to the right

Explanation:

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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Advanced Geometry : How to graph inverse variation

Study concepts, example questions & explanations for Advanced Geometry

All Advanced Geometry Resources

Example Questions

Example Question #1 : How To Graph Inverse Variation

Example Question #2 : Graphing Inverse Variation

Example Question #3 : Graphing Inverse Variation

Example Question #4 : Graphing Inverse Variation

Example Question #2 : How To Graph Inverse Variation

Example Question #191 : Algebra

Example Question #1 : How To Graph Inverse Variation

Example Question #1 : How To Graph Inverse Variation

Example Question #1 : How To Graph Inverse Variation

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