Download - Rational Function
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What is an asymptote?
• An asymptoteasymptote is an imaginary line being approached but never touched or intersected by a graph as it goes through infinity.
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Example 1: Sketch the graph of a rational function
g xx
( ) 3
2V. A : x = 2
H. A : y = 0
g (0) = - 3/2
g (3) = 3
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Example 2: Sketch the graph of
f xx
x x( )
2 2V. A : x = 2, x = -1
H. A : y = 0
f(0) = 0
f(1) = - 1/2
f(-2) = - 1/2
f(3) = 3/4
![Page 5: Rational Function](https://reader033.vdocuments.site/reader033/viewer/2022061202/547c277a5806b5fe3f8b472a/html5/thumbnails/5.jpg)
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The square root function is actually the inverse operation of the quadratic function.
xxf )(
x f(x)
0
1
4
9
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The square root function is actually the inverse operation of the quadratic function.
xxf )(
x f(x)
0 0
1
4
9
![Page 8: Rational Function](https://reader033.vdocuments.site/reader033/viewer/2022061202/547c277a5806b5fe3f8b472a/html5/thumbnails/8.jpg)
The square root function is actually the inverse operation of the quadratic function.
xxf )(
x f(x)
0 0
1 1
4
9
![Page 9: Rational Function](https://reader033.vdocuments.site/reader033/viewer/2022061202/547c277a5806b5fe3f8b472a/html5/thumbnails/9.jpg)
The square root function is actually the inverse operation of the quadratic function.
xxf )(
x f(x)
0 0
1 1
4 2
9
![Page 10: Rational Function](https://reader033.vdocuments.site/reader033/viewer/2022061202/547c277a5806b5fe3f8b472a/html5/thumbnails/10.jpg)
The square root function is actually the inverse operation of the quadratic function.
xxf )(
x f(x)
0 0
1 1
4 2
9 3
![Page 11: Rational Function](https://reader033.vdocuments.site/reader033/viewer/2022061202/547c277a5806b5fe3f8b472a/html5/thumbnails/11.jpg)
The square root function is actually the inverse operation of the quadratic function.
xxf )(
x f(x)
0 0
1 1
4 2
9 3
xxf )(
x f(x)
0
1
4
9
![Page 12: Rational Function](https://reader033.vdocuments.site/reader033/viewer/2022061202/547c277a5806b5fe3f8b472a/html5/thumbnails/12.jpg)
The square root function is actually the inverse operation of the quadratic function.
xxf )(
x f(x)
0 0
1 1
4 2
9 3
xxf )(
x f(x)
0 0
1
4
9
![Page 13: Rational Function](https://reader033.vdocuments.site/reader033/viewer/2022061202/547c277a5806b5fe3f8b472a/html5/thumbnails/13.jpg)
The square root function is actually the inverse operation of the quadratic function.
xxf )(
x f(x)
0 0
1 1
4 2
9 3
xxf )(
x f(x)
0 0
1 -1
4
9
![Page 14: Rational Function](https://reader033.vdocuments.site/reader033/viewer/2022061202/547c277a5806b5fe3f8b472a/html5/thumbnails/14.jpg)
The square root function is actually the inverse operation of the quadratic function.
xxf )(
x f(x)
0 0
1 1
4 2
9 3
xxf )(
x f(x)
0 0
1 -1
4 -2
9
![Page 15: Rational Function](https://reader033.vdocuments.site/reader033/viewer/2022061202/547c277a5806b5fe3f8b472a/html5/thumbnails/15.jpg)
The square root function is actually the inverse operation of the quadratic function.
xxf )(
x f(x)
0 0
1 1
4 2
9 3
xxf )(
x f(x)
0 0
1 -1
4 -2
9 -3
![Page 16: Rational Function](https://reader033.vdocuments.site/reader033/viewer/2022061202/547c277a5806b5fe3f8b472a/html5/thumbnails/16.jpg)
Remember that it is not possible to get the square root of a negative number, therefore the values that are chosen for x in the table of values must be strategic.
xxf )(
x f(x)0 0-1 Error-4 Error-9 Error
Error
x f(x)0 01 12 1.43 2.8
It is possible however, to use non-perfect squares with this function. You will end uo with an irrational y-value that needs to be rounded off but that’s okay. It just makes it a little more awkward to plot on the graph.
xxf )(
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If we play with parameter ‘a’, we can see its effect on the resulting graph.
xxf )( a = 1xxf 2)( a = 2
21
;21
)( axxf xxf )( a = -1
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If we play with parameter ‘b’, we can see its effect on the resulting graph.
xxf )( a = 1 xxf 2)( b = 2
21
;21
)( bxxf xxf )( b = -1
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The signs of parameters a and b determine which way the square root function moves from its vertex.
xxf )( a = +; b = +
xxf )( a = -; b = +
xxf )( a = -; b = -xxf )( a = +; b = -
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THANK YOU !!!
---Ms. Jerlyn Fernandez