Download Functions Involving Square Roots

12.1
Functions Involving Square
Roots
Goal
Evaluate and graph a
function involving
square roots.
How fast can a dinosaur walk?
The maximum walking speed of a
dinosaur is a function of the length
of its leg. In Exercise 57 you will use
a function involving a square root to
compare the maximum walking
speeds for two species of dinosaurs.
Key Words
• square root function
• domain
• range
The square root function is defined by the equation
y x.
Its domain is all nonnegative numbers, and its range is all nonnegative numbers.
Understanding the square root function will help you work with other functions
involving square roots.
EXAMPLE
Student Help
STUDY TIP
Recall that the square
root of a negative
number is undefined.
x can be evaluated
only when x ≥ 0.
1
Evaluate Functions Involving Square Roots
Find the domain of y 2x. Use several values in the domain to make
a table of values for the function.
Solution
A square root is defined only when
the radicand is nonnegative. Therefore
the domain of y 2x consists of
all nonnegative numbers. A table of
values for x 0, 1, 2, 3, 4, and 5 is
shown at the right.
x
y
0
y 20 0
1
y 21 2
2
y 22 ≈ 2.8
3
y 23 ≈ 3.5
4
y 24 4
5
y 25 ≈ 4.5
Evaluate Functions Involving Square Roots
Find the domain of the function. Then use several values in the domain
to make a table of values for the function.
1. y x
692
Chapter 12
2. y 3x
Radicals and More Connections to Geometry
3. y 2
x
4. y x 1