Squaring and Rooting: Inverses
Squaring and Rooting: Inverses
•'^^SJSiniSBf^oive each equation for x. Remember: These equations usually have two solutions. A) x ' + 2 1 = 70
B ) 4 x ' - 1 2 = 13
1. Review of Quadratic Functions A. For the equation y = x ^ 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 ) ' + 4 = 40
y = x^ X
y
-3 -2
4
-1 0 -4
4
1 C. Is this equation a function? Explain. 2. Inverse with Coordinates . 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 3
Inverse X
y -3 -2 -1
B. Is this inverse a function? Explain.
0 1 2 3
3. Inverse with Algebra Remember that another way Equation: to find an inverse is to switch the X and y variables in an Inverse: equation, then solve for the "new" y. Solve: A. Use this algebraic method to find the inverse of y = x^. Notation: f-\x)
y = x^
=
B. Use a calculator to help you sketch the graph of this inverse equation in the box below.
Does this graph match your answer from #2? Explain.
Squaring and Rooting: Inverses These two relations are inverses of one another. Graph:
[
/
What are the properties of inverses?
1; ,
•
Graph: y
Their graphs are over the
X
line Equation:
•
Their equations have the
Equation:
switched Shape:
Shape:
What's the " P R O B L E M " with this graph? This graph is So, normally... We just graph the
and call it the GrapfV.
function. Domain:
Parent function:
^ Y n i r a n nnlu i i ^ p \ w u 1 Willy
Table: X
y
0 1 4 9
0 1 2 3
u o ^
values for
.)
Range: 2
4
6
8
(You will only get answers for
.)
Squaring and Rooting: Inverses Review of Quadratic Transformations
y = 2x^-2
X
y
-2 A. For the equation above, complete the table. Then plot points to construct the graph.
-1 0 1 2
B. This graph is a transformation of the parent graph y = . Tell how each constant in the equation changes the graph of the parent function. •
What effect does the " - 2 " have on the graph?
•
What effect 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 .
X
y -2 -1 0 1 2
B. Is this inverse a function? Explain.
6. Inverse with Algebra Remember that another way Equation: to find an inverse is to switch the X and y variables in an Inverse: equation, then solve for the "new" y. Solve:
y = 2x'-2
B. Use a calculator to help you sketch the graph of this inverse equation in the box below.
A. Use this algebraic method to find the inverse of y = 2x^-2. Notation:
Does this graph match your answer from #5? Explain.
Squaring and Rooting: Inverses 7. Review of Quadratic Transformations
y = (x-3)'-1
X
y
0 A. For the equation above, complete the table. Then plot points to construct the graph.
1 2 3
B. This graph is a transformation of the parent graph y = Tell how each constant in the equation changes the graph of the parent function.
4 5 6
•
What effect does the " - 3 " have on the graph?
•
What effect does the
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)^ - 1 .
X
y 0 1 2 3 4
B. Is this inverse a function? Explain.
5 6
9. Inverse with Algebra Remember that another way Equation: to find an inverse is to switch the X and y variables in an Inverse: equation, then solve for the "new" y. Solve:
y = (x-3)'-1
B. Use a calculator to help you sketch the graph of this inverse equation in the box below.
A. Use this algebraic method to find the inverse of y = (x-3)'-1. Notation:
Does this graph match your answer from #8? Explain.
•'^^SJSiniSBf^oive each equation for x. Remember: These equations usually have two solutions. A) x ' + 2 1 = 70
B ) 4 x ' - 1 2 = 13
1. Review of Quadratic Functions A. For the equation y = x ^ 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 ) ' + 4 = 40
y = x^ X
y
-3 -2
4
-1 0 -4
4
1 C. Is this equation a function? Explain. 2. Inverse with Coordinates . 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 3
Inverse X
y -3 -2 -1
B. Is this inverse a function? Explain.
0 1 2 3
3. Inverse with Algebra Remember that another way Equation: to find an inverse is to switch the X and y variables in an Inverse: equation, then solve for the "new" y. Solve: A. Use this algebraic method to find the inverse of y = x^. Notation: f-\x)
y = x^
=
B. Use a calculator to help you sketch the graph of this inverse equation in the box below.
Does this graph match your answer from #2? Explain.
Squaring and Rooting: Inverses These two relations are inverses of one another. Graph:
[
/
What are the properties of inverses?
1; ,
•
Graph: y
Their graphs are over the
X
line Equation:
•
Their equations have the
Equation:
switched Shape:
Shape:
What's the " P R O B L E M " with this graph? This graph is So, normally... We just graph the
and call it the GrapfV.
function. Domain:
Parent function:
^ Y n i r a n nnlu i i ^ p \ w u 1 Willy
Table: X
y
0 1 4 9
0 1 2 3
u o ^
values for
.)
Range: 2
4
6
8
(You will only get answers for
.)
Squaring and Rooting: Inverses Review of Quadratic Transformations
y = 2x^-2
X
y
-2 A. For the equation above, complete the table. Then plot points to construct the graph.
-1 0 1 2
B. This graph is a transformation of the parent graph y = . Tell how each constant in the equation changes the graph of the parent function. •
What effect does the " - 2 " have on the graph?
•
What effect 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 .
X
y -2 -1 0 1 2
B. Is this inverse a function? Explain.
6. Inverse with Algebra Remember that another way Equation: to find an inverse is to switch the X and y variables in an Inverse: equation, then solve for the "new" y. Solve:
y = 2x'-2
B. Use a calculator to help you sketch the graph of this inverse equation in the box below.
A. Use this algebraic method to find the inverse of y = 2x^-2. Notation:
Does this graph match your answer from #5? Explain.
Squaring and Rooting: Inverses 7. Review of Quadratic Transformations
y = (x-3)'-1
X
y
0 A. For the equation above, complete the table. Then plot points to construct the graph.
1 2 3
B. This graph is a transformation of the parent graph y = Tell how each constant in the equation changes the graph of the parent function.
4 5 6
•
What effect does the " - 3 " have on the graph?
•
What effect does the
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)^ - 1 .
X
y 0 1 2 3 4
B. Is this inverse a function? Explain.
5 6
9. Inverse with Algebra Remember that another way Equation: to find an inverse is to switch the X and y variables in an Inverse: equation, then solve for the "new" y. Solve:
y = (x-3)'-1
B. Use a calculator to help you sketch the graph of this inverse equation in the box below.
A. Use this algebraic method to find the inverse of y = (x-3)'-1. Notation:
Does this graph match your answer from #8? Explain.
