Algebra 2: Unit 4 Lesson 1
Without graphing, fill in the table below for the function y =
x
Name ____________________________________________________________
1
and sketch the graph to the right.
x
y
-5
-4
-3
-2
-1.7
-1
-0.5
-0.2
-0.1
-0.001
0
0.001
0.1
0.2
0.5
0.7
1
1.2
1.5
2
3
4
5
An asymptote is a line that the curve approaches but does not quite reach.
The vertical asymptote of this function is x = 0.
The horizontal asymptote of this function is y = 0.
Once you have sketched the graph by
hand, check the graph of the function
using your graphing calculator.
Questions:
1) What is happening to the values
of y as x gets very small?
2) What is happening to the values
of y as x gets very large?
3) As x is getting close to zero from
the left, what is y doing?
4) As x is getting close to zero from
the right, what is y doing?
5) On the graph, label each
asymptote with its equation.
6) On the graph, label (1,1) and (-1,1) to use as reference points for
transformations.
Transforming y =
1
1
+k
into y = a
(x - h)
x
7. Based transformations of parent functions, describe what you transformations you would expect below in the graph of y =
y=
1
-3
x +1
1æ 1 ö
y= ç
÷
2 è x +1ø
æ 1ö
y = -ç ÷ + 2
è xø
æ 1 ö
y = 2ç
è x - 2 ÷ø
æ 1 ö
y = -ç
è x - 1÷ø
y=
1
-3
x -1
æ 1ö
y = -2 ç ÷ + 2
è xø
æ 1 ö
y = -2 ç
è x + 1÷ø
Shift _______
units right
Shift _______
units left
Shift _______
units up
Shift _______
down
Vertical
stretch of
factor ______
Vertical
compression
of factor
______
Vertical flip?
8. Last Step!! Match the correct equation with the graphs your group is given. Write the equation under each graph.
As you match the correct equation, check on the graphing calculator!
1
x
1 æ 1ö
y= ç ÷ +2
2 è xø