Domain and Range of a Function

Domain and Range of a Function

Dr. Rowlett

Multiple Choice

If f(x) is a polynomial, its domain is...

• all real numbers.

• zero to infinity

• underfined

• all real numbers, except zero.

Open Ended

A polynomial function takes the form

 $f\left(x\right)=a_nx^n+a_{\left(n-1\right)}x^{\left(n-1\right)}+...+a_0$  where n is a nonnegative integer. 

If you graph a function, how many times may a vertical line cross at any point on the graph?

Multiple Choice

What number is not allow in the denominator of a fraction?

• 0

• pi

• negative integers

• fractions

Multiple Choice

Consider

 $f\left(x\right)=\frac{1}{x}$  . What is the domain of the function?

• All real numbers except 0.

• 0

• (negative infinity, infinity)

• all real numbers

Multiple Choice

Consider

 $f\left(x\right)=\frac{x+2}{x-2}$  The domain is all real numbers, except...

• -2

• 2

• 0

• 4

Multiple Choice

Let

 $f\left(x\right)=3x^2-4x+2$  Its domain is...

• All real numbers

• All real numbers except zero

• negative infinity

• positive infinity

Multiple Select

Suppose

 $f\left(x\right)=\left(x+4\right)^{-2}$  Select all that are true.

• f(x) is a polynomial

• Its domain is all real numbers, except -4

• f(x) may be rewritten as  $\frac{1}{\left(x+4\right)^2}$  

• The domain is all real numbers

Multiple Choice

 $f\left(x\right)=4x^3\$  is a polynomial. Respond to that statement.

• True, because its exponent is a nonnegative integer.

• True, because it isn't a fraction.

• False

Multiple Select

 $f\left(x\right)=\frac{3x}{\left(x+4\right)}$  Select all correct statements.

• The domain is all real numbers except  0.

• This is not a polynomial because there is a variable in the denominator.

• The domain is all real numbers, except -4.

• The line x = -4 is a vertical asymptote.

Multiple Choice

One way to determine the domain of a function is to find values that will make the denominator...

• negative

• zero

• infinity

• positive

Multiple Choice

What is the range of

 $f\left(x\right)=3x+1$  when x = 2.

• 1

• 3

• 2

• 7

Multiple Choice

What is the range when the domain is 2, for

 $f\left(x\right)=2x^3-1$  

• 13

• 15

• 13

• -15

Multiple Choice

What is the range when x = 4, for

 $f\left(x\right)=\frac{-4}{x-4}$  

• 0

• -4

• -1/4

• undefined

Open Ended

Often, we have to factor to find the domain of a function.

Which value, x or y, represents the domain.

Multiple Select

For

 $f\left(x\right)=\frac{2x}{\left(x-9\right)\left(x+4\right)}$  the domain is all real numbers except....

• 0

• 9

• 4

• -4

Multiple Select

Think! If

 $f\left(x\right)=\frac{1}{x^2-4}$  , its domain is all real number except

• 0

• 2

• 4

• -2

Open Ended

This video shows how to find the domains of rational functions.

We never divide by what number?

Open Ended

This last video reinforces today's objective, finding the domain of polynomial functions, but extends to root functions, too. Can you explain the range of a function?