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ACT Math : How to graph inverse variation

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Example Questions

Example Question #193 : Algebra

A triangle is made up of the following points:

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

What are the points of the inverse triangle?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 : Graphing

Electrical power can be generated by wind, and the magnitude of power will depend on the wind speed. A wind speed of $\displaystyle v$ (in $\tiny m/s$ $\displaystyle \tiny m/s$) will generate a power of $v^{2}+4v$ $\displaystyle v^{2}+4v$ watts $\displaystyle watts$. What is the minimum wind speed needed in order to power a device that requires $\displaystyle 96$ watts $\displaystyle watts$?

Possible Answers:

5 m/s $\displaystyle 5 m/s$

9 m/s $\displaystyle 9 m/s$

8 m/s $\displaystyle 8 m/s$

3 m/s $\displaystyle 3 m/s$

6 m/s $\displaystyle 6 m/s$

Correct answer:

8 m/s $\displaystyle 8 m/s$

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 $\displaystyle 96$ watts $\displaystyle watts$.

Alternatively, one could set up the equation,

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

$\displaystyle ax^2+bx+c$.

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

Thus the following factoring would solve this problem.

$\displaystyle (v+12)(v-8)=0$

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

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

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

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

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Example Question #2 : How To Graph Inverse Variation

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

Possible Answers:

$\displaystyle 4$ units up.

$\displaystyle 5$ units down.

$\displaystyle 4$ units down.

$\displaystyle 4$ units to the right.

$\displaystyle 4$ units to the left.

Correct answer:

$\displaystyle 4$ units to the left.

Explanation:

The (+4) $\displaystyle (+4)$ inside the argument has the effect of shifting the graph $\displaystyle 4$ 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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ACT Math : How to graph inverse variation

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #193 : Algebra

Example Question #1 : Graphing

Example Question #2 : How To Graph Inverse Variation

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