Graphing Rational Functions
Graphing Rational Functions
Graphing Rational Functions
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Kuta Software - Infinite Algebra 2<br />
Name___________________________________<br />
<strong>Graphing</strong> <strong>Rational</strong> <strong>Functions</strong><br />
Date________________<br />
Period____<br />
Identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asymptote of<br />
each.<br />
1)<br />
f ( x) =<br />
<br />
x x<br />
2)<br />
f ( x) =<br />
x<br />
x<br />
3)<br />
f ( x) =<br />
x x x<br />
x x<br />
4)<br />
f ( x) =<br />
x x<br />
x x<br />
Identify the points of discontinuity, holes, vertical asymptotes, and horizontal asymptote of each. Then<br />
sketch the graph.<br />
5)<br />
<br />
f ( x) = <br />
x x<br />
6)<br />
f ( x) =<br />
x<br />
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7)<br />
f ( x) =<br />
x<br />
x<br />
8)<br />
f ( x) =<br />
x x<br />
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y<br />
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y<br />
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x x<br />
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9) f ( x) =<br />
10) f ( x) =<br />
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11)<br />
f ( x) =<br />
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12)<br />
f ( x) =<br />
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13)<br />
f ( x) =<br />
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14)<br />
f ( x) =<br />
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-1-<br />
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Kuta Software - Infinite Algebra 2<br />
<strong>Graphing</strong> <strong>Rational</strong> <strong>Functions</strong><br />
Name___________________________________<br />
Date________________<br />
Period____<br />
Identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asymptote of<br />
each.<br />
<br />
x<br />
1) f ( x) =<br />
Discontinuities: , 2) f ( x) =<br />
x x<br />
Vertical Asym.: x, x<br />
x<br />
Discontinuities: <br />
Vertical Asym.: x<br />
Holes: None<br />
Holes: None<br />
Horz. Asym.: y<br />
Horz. Asym.: y<br />
X-intercepts: None<br />
X-intercepts: <br />
x x x<br />
x x<br />
3) f ( x) =<br />
Discontinuities: , 4) f ( x) =<br />
Discontinuities: , <br />
x x<br />
Vertical Asym.: x, x<br />
x x<br />
Vertical Asym.: x<br />
Holes: None<br />
Holes: x<br />
Horz. Asym.: None<br />
X-intercepts: , , <br />
Horz. Asym.: y <br />
X-intercepts: <br />
Identify the points of discontinuity, holes, vertical asymptotes, and horizontal asymptote of each. Then<br />
sketch the graph.<br />
5)<br />
<br />
f ( x) = <br />
x x<br />
6)<br />
f ( x) =<br />
x<br />
x<br />
<br />
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<br />
y<br />
Discontinuities: , <br />
Vertical Asym.: x, x<br />
Holes: None<br />
Horz. Asym.: y<br />
<br />
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<br />
y<br />
Discontinuities: <br />
Vertical Asym.: x<br />
Holes: None<br />
Horz. Asym.: y <br />
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x<br />
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7)<br />
f ( x) =<br />
x<br />
x<br />
8)<br />
f ( x) =<br />
x x<br />
x x<br />
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y<br />
Discontinuities: <br />
Vertical Asym.: x<br />
Holes: None<br />
Horz. Asym.: y <br />
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y<br />
Discontinuities: , <br />
Vertical Asym.: x<br />
Holes: x<br />
Horz. Asym.: None<br />
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x<br />
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x
-2-<br />
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9)<br />
x x<br />
f ( x) =<br />
x x<br />
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y<br />
Discontinuities: , <br />
Vertical Asym.: x, x<br />
Holes: None<br />
Horz. Asym.: y<br />
10)<br />
x x<br />
f ( x) =<br />
x x<br />
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y<br />
Discontinuities: , <br />
Vertical Asym.: x, x<br />
Holes: None<br />
Horz. Asym.: None<br />
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11)<br />
f ( x) =<br />
x x<br />
x<br />
12)<br />
f ( x) =<br />
x<br />
x<br />
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y<br />
Discontinuities: <br />
Vertical Asym.: x<br />
Holes: None<br />
Horz. Asym.: None<br />
<br />
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y<br />
Discontinuities: <br />
Vertical Asym.: x<br />
Holes: None<br />
Horz. Asym.: y <br />
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13)<br />
f ( x) =<br />
x x<br />
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14)<br />
f ( x) =<br />
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x<br />
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y<br />
Discontinuities: , <br />
Vertical Asym.: x<br />
Holes: x<br />
Horz. Asym.: y<br />
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y<br />
Discontinuities: <br />
Vertical Asym.: x<br />
Holes: None<br />
Horz. Asym.: y<br />
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x<br />
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