Radical Expressions and Radical Functions Objective: Analyze graphs of rational functions and...
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Transcript of Radical Expressions and Radical Functions Objective: Analyze graphs of rational functions and...
Radical Expressions and Radical Functions
Objective: Analyze graphs of rational functions and evaluate radical
expressions.
5 up 5left 5by stretch vert on x flip5,by stretch vert
51by n compressio horiz. 5by stretch horiz.
Example 1
Example 1
Try This
• Find the domain of 185)( xxg
Try This
• Find the domain of
• The domain of g(x) is
185)( xxg
518
185
0185
x
x
x
Transformations
Example 2
Example 2
Try This
• For each function, describe the transformations applied to .xy
213 xy 42 xy
Try This
• For each function, describe the transformations applied to .
• Vertical stretch of 3, Reflect on x-axis, down 2, to the right 1. horiz. Comp. of ½ up 4.
xy
213 xy 42 xy
Example 3
Example 3
Example 3
Try This
• Find the inverse of . Then graph the function and its inverse together.
432 xxy
Try This
• Find the inverse of . Then graph the function and its inverse together.
432 xxy
)4(30
43
43
2
2
2
xyy
yyx
xxy
)4(
3
1
xc
b
a
Try This
• Find the inverse of . Then graph the function and its inverse together.
432 xxy
)4(30
43
43
2
2
2
xyy
yyx
xxy
2
4253
2
16493
2
)4)(1(4)3(3 2 xxx
)4(
3
1
xc
b
a
Try This
• Find the inverse of . Then graph the function and its inverse together.
432 xxy
2
4253 x432 xxy
Example 4
Example 5
Example 5
Try This
• Evaluate
1012523 2862
3
Try This
• Evaluate
1012523 2862
3
01010
10)5(2
262)4(6
226 2
2;063 xx
2down 4,right
3 ofstretch vert.5 up3,left
of comp. horiz. 21
yx
yx
yx
3
3
32
2
8)5(412
171027
1033 2
Homework
• Pages 525-526• 11-29 odd• 37-51 odd