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Algebra 2 Honors
Section 6.3 Notes: Square Root Functions and Inequalities
Square Root Function: a function that contains the square root of a variable.
*A type of radical function.
Domain and Range of Square Root Functions:
Domain: The expression under a radical has to be > 0. So, take the expression under the radical and set it ≥ 0 and that will be your
domain.
Range: Take the number from your domain inequality and substitute it into the expression. Your range will be all numbers ≥ or <
that result.
Example 1: Identify the domain and range of f  x   x  1.
Example 2: Identify the domain and range of f  x   2 x  1  3.
Example 2: Identify the domain and range of f  x   4 3x  1  5.
Example 3: Graph each function State the domain and range.
a) f  x   3 x  4  2.
b)
Example 5: Graph the function f  x   3 x  2  3.
a)
b)
c)
d)
Square Root Inequalities:
f  x    x  5  6.
*An inequality involving square roots.
*Graph using same method as other inequalities.
-Solid or dashed line???
-Shade above or below??? (Test point.)
*From endpoint, shade straight up/down.
Example 6: Graph y   x  1  2.
Example 7: Graph y  2 x  4.
a)
b)
c)
d)
Example 8: When an object is spinning in a circular path of radius 2 meters with velocity v, in meters per second, the centripetal
acceleration a, in meters per second squared, is directed toward the center of the circle. The velocity v and acceleration a of the object
are related by the function v  2.a
a. Graph the function in the domain {a|a ≥ 0}.
b. What would be the centripetal acceleration of an object spinning along the circular path with a velocity of 4 meters per second?
Domain of Cube Root Functions:
Domain: What type of numbers can/cannot be underneath a cube root?
*Any # can be put under a cube root!
Therefore, the domain of cube root functions is all real numbers.
Range of Cube Root Functions:
Range: What type of numbers will result from cube rooting a number?
*Answers could be ANY number!
Therefore, the range of cube root functions is all real numbers.
Example 9: Graph the function f  x   3 x . State the domain and range.
(Parent function for cubed roots)
Example 10: Graph the function and state the domain and range.
a)
f  x   3 x  1  3.
c)
f ( x)   3 x  3
b)
f  x   2 3 x  2  1.