Name _____________________________________
Algebra 2: 8.6 – Introduction Rational Functions
1. For each description below, write an equation and graph each transformation from the parent
function f  x  
1
.
x
a. Translate the graph left 3 units and down 4
units.
b. Vertically dilate the graph by a scale factor of
3 and translate right 2 units.
Equation:
Equation:
2. For each rational function below, write the equations of the asymptotes.
a. y 
2
x
b. y 
1
x3
c. y  
d. y 
1
5
x 1
e. y 
2
6
x2
f. y 
3
x
4
1
x2
3. Solve each equation for x.
a.
6
 2
x 5
b.
4
1

2x  5
2
c. 2 
2 x  14
x 1
4. For each of the equations, describe the transformation(s) from the parent function f  x  
1
and
x
graph the transformed function. Then, state the domain, range, asymptotes , and end behavior.
a. y  3 
1
x
b. y 
2
1
x4
c. y 
3
x2
Transformations:
Transformations:
Transformations:
Domain:
Domain:
Domain:
Range:
Range:
Range:
Asymptotes:
Asymptotes:
Asymptotes:
End Behavior:
End Behavior:
End Behavior:
a. 𝑦 = 3 +
1
𝑥−5
b. 𝑦 = −
4
𝑥
c. 𝑦 =
3
−
𝑥+3
4
Transformations:
Transformations:
Transformations:
Domain:
Domain:
Domain:
Range:
Range:
Range:
Asymptotes:
Asymptotes:
Asymptotes:
End Behavior:
End Behavior:
End Behavior: