Download Section 8.6 - Souderton Math

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Transcript
8.6 Radical Expressions and
Radical Functions
Objective:
Analyze the graphs of radical functions,
and evaluate radical expressions. Find
the inverse of a quadratic function.
The square root of a number, x is a number
when multiplied produces the given number, x.
The domain of the square root function f ( x)  x
does not include negative numbers.
The domain of f ( x)  x
is all nonnegative
real numbers, and the range is all nonnegative
real numbers.
The domain is
all real
numbers that
do not make
2x-5 negative
2x  5
x  5/ 2
B.
Find the domain of
g ( x)  5 x  18
5x  18  0
5x  18
x  18 / 5
h( x)  x  2 x  15
2
x  2 x  15  0
2
GreatOR
( x  5)( x  3)  0
x ≥ 5 or x ≤ -3
x ≤ -3
x≥5
The transformations for the square-root parent
function, y=√x are summarized below
Vertical stretch
or compression
by a factor of | a|,
for a<0, the
graph is a
reflection across
the x-axis
Vertical translation k
units up for k>0 and | k |
units down for k<0.
y  a b( x  h)  k
Horizontal stretch or
compression by a factor of
| 1/b | for b<o, the graph is a
reflection across the y axis
Horizontal translation h
units to the right for h>0
and h units to the left for
h<0
c. * y 
2x 1  3
d. *
y  3 x 1  2
You can find the inverse of a
function by interchanging x and y,
the solving for y.
c.
*
 2  125  10
3
D.
6( 8 )  2
3
2
=6(2)²+2
=6(4)+2
=26
Homework
Integrated Algebra II- Section 8.6 Level A
Honors Algebra II- Section 8.6 Level B