Squaring and Rooting Inverses

advertisement
Algebra 2
HS Mathematics
Unit: 06 Lesson: 01
Squaring and Rooting: Inverses
Warm-Up
Solve each equation for x. Remember: These equations usually have two solutions.
A) x 2  21  70
B) 4 x 2  12  13
1. Review of Quadratic Functions
A. For the equation y = x 2 , complete
the table. Then plot points to
construct the graph.
B. If the domain of the equation is
3, 2, 1,0,1,2,3 , then what
would be the range?
C) ( x  3)2  4  40
y = x2
x
y
-3
-2
4
-1
0
-4
4
1
2
C. Is this equation a function?
Explain.
-4
3
2. Inverse with Coordinates
A. Recall that an inverse can be
formed by switching the x- and ycoordinates in a relation. Use this
method to make a table and graph
for the inverse of y = x 2 .
Inverse
x
y
-3
-2
4
-1
B. Is this inverse a function?
Explain.
0
1
-4
4
2
3
3. Inverse with Algebra
Remember that another way
to find an inverse is to switch
the x and y variables in an
equation, then solve for the
“new” y.
A. Use this algebraic method
to find the inverse of
y = x2 .
©2012, TESCCC
Equation:
Inverse:
y = x2
____ = ____2
-4
B. Use a calculator to help you sketch
the graph of this inverse equation
in the box below.
Solve:
Notation: f - 1( x ) =
Does this graph match your answer
from #2? Explain.
Editable Resource Document (ERD)–Content may be modified (DULA terms and conditions still apply)
Algebra 2
HS Mathematics
Unit: 06 Lesson: 01
Squaring and Rooting: Inverses
These two relations are inverses of one another.
Graph:
What are the properties of
inverses?
y

Graph:
y
Their graphs are
_________________ over the
x
x
line ___________
Equation:

Their equations have the
Equation:
_______________ switched
Shape:
Shape:
What’s the “PROBLEM” with this graph?
This graph is ___________ a ________________!
So, normally…
We just graph the _______ ___________ and call it the _____________ _____________ function.
Graph:
Domain:
Parent function:
f (x) = x
Table:
x
0
1
4
9
__________________
(You can only use ____________
y
0
1
2
3
values for _____.)
2
Range:
2
4
6
8
__________________
(You will only get ____________
answers for _____.)
©2012, TESCCC
Editable Resource Document (ERD)–Content may be modified (DULA terms and conditions still apply)
Algebra 2
HS Mathematics
Unit: 06 Lesson: 01
Squaring and Rooting: Inverses
4. Review of Quadratic Transformations
x
y  2x 2  2
-2
A. For the equation above,
-1
complete the table. Then plot
0
points to construct the graph.
1
2
y
4
-4
4
B. This graph is a transformation of the parent graph
y = x 2 . Tell how each constant in the equation
changes the graph of the parent function.

What affect does the “−2” have on the graph?

What affect does the “2” coefficient have on the
graph?
5. Inverse with Coordinates
A. Again, recall that an inverse
can be formed by switching
the x- and y- coordinates in a
relation. Use this method to
make a table and graph for
the inverse of y  2x 2  2 .
x
-4
y
-2
-1
0
1
2
B. Is this inverse a function? Explain.
4
-4
4
-4
6. Inverse with Algebra
Remember that another way
to find an inverse is to switch
the x and y variables in an
equation, then solve for the
“new” y.
Equation:
Inverse:
y  2x 2  2
B. Use a calculator to help you
sketch the graph of this
inverse equation in the box
below.
Solve:
A. Use this algebraic method
to find the inverse of
y  2x 2  2 .
Notation:
©2012, TESCCC
Does this graph match your
answer from #5? Explain.
Editable Resource Document (ERD)–Content may be modified (DULA terms and conditions still apply)
Algebra 2
HS Mathematics
Unit: 06 Lesson: 01
Squaring and Rooting: Inverses
7. Review of Quadratic Transformations
y  ( x  3)2  1
x
0
A. For the equation above,
complete the table. Then plot
points to construct the graph.
y
1
2
4
3
B. This graph is a transformation of
the parent graph y = x 2 . Tell
how each constant in the
equation changes the graph of
the parent function.
4
-4
6
-4

What affect does the “−3” have on the graph?

What affect does the “−1” have on the graph?
8. Inverse with Coordinates
A. Again, recall that an inverse
can be formed by switching
the x- and y- coordinates in a
relation. Use this method to
make a table and graph for
the inverse of y  ( x  3)2  1 .
4
5
x
y
0
1
2
4
3
4
B. Is this inverse a function?
Explain.
-4
4
5
6
-4
9. Inverse with Algebra
Remember that another way
to find an inverse is to switch
the x and y variables in an
equation, then solve for the
“new” y.
Equation:
Inverse:
y  ( x  3)2  1
B. Use a calculator to help you
sketch the graph of this
inverse equation in the box
below.
Solve:
A. Use this algebraic method
to find the inverse of
y  ( x  3)2  1 .
Notation:
©2012, TESCCC
Does this graph match your
answer from #8? Explain.
Editable Resource Document (ERD)–Content may be modified (DULA terms and conditions still apply)
Download
Related flashcards

Algebra

20 cards

Polynomials

21 cards

Abstract algebra

19 cards

Ring theory

15 cards

Category theory

14 cards

Create Flashcards