Graphing Simple Rational Functions - Kuta Software

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7) f (x) = 3 x + 1 x
y
8 Vertical Asym.: x = 0
Horz. Asym.: y = 1
6
Domain:
All reals except 0
4
Range:
All reals except 1
2
8) f (x) =
2
x − 3 + 1
y
8 Vertical Asym.: x = 3
Horz. Asym.: y = 1
6
Domain:
All reals except 3
4
Range:
All reals except 1
2
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
x
9) f (x) = − 4
x + 1 + 1
10) f (x) = 4 x + 2 x
y
8 Vertical Asym.: x = −1
Horz. Asym.: y = 1
6
Domain:
All reals except −1
4
Range:
All reals except 1
2
y
8 Vertical Asym.: x = 0
Horz. Asym.: y = 2
6
Domain:
All reals except 0
4
Range:
All reals except 2
2
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
x
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
Critical thinking question:
11) Write a function of the form f (x) =
1
Many answers. Ex: f (x) =
x − 25
a
x − h
+ k with a vertical asymptote at x = 25
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