Domain and Range (Advanced)

Domain and Range

Two more examples of domain and range

When there is a white dot, that value is not included, a black dot is included

On this graph, that means -3 is not included but the value of 1 is so the domain is -3

Domain and range are all the reals

Linear Function

Domain is all the reals
Range depends on the concavity and the value of the y-coordinate of its vertex

Quadratic Function

Domain is all the reals.
Range depends on the function

Polynomial Function

Functions with Restrictions on Domain

Its domain are the values where the radicant is zero or positive

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Radical Functions

Its domain are the values where the denominator is not zero

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Rational Functions

Multiple Choice

What is the domain?

• -3 < y ≤ 3

• -4 ≤ y ≤ 5

• -4 ≤ x ≤ 5

• -3 < x ≤ 3

Multiple Choice

What is the range?

• -4 < x ≤ 5

• -4 ≤ x < 5

• -3 < y < 3

• -3 ≤ y ≤ 3

Match

Match the following relations with the given RANGES

• $$\left\{\left(-1,2\right),\left(0,3\right),\left(1,-1\right),\left(7,0\right)\right\}$$

• $$\left\{-1,0,2,3\right\}$$

• $$\left\{-4\le y<2\right\}$$

• $$y>0$$

• $$\left\{-1,0,1,1.46,2\right\}$$

Multiple Choice

What is the range in inequality notation?

• ( -4 , 4 )

• [ 1 , -3 )

• -4 < x < 4

• 1 ≥ y > -3

Multiple Choice

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

• (-infinity, infinity)

• [-1, infinity)

• (1, infinity)

• [1, infinity)

Multiple Choice

What is the domain of the graph of the function $$f\left(x\right)=-7-\sqrt{x+4}$$ ?

• (-infinity, infinity)

• (-7, infinity)

• [-4, infinity)

• (-4, infinity)

Multiple Choice

What is the range of this graph?

• y ≥ -1

• y ≤ -1

• y ≥ 0

• y ≤ 0

Multiple Choice

Which of the following correctly describes the domain and range for the function graphed?

• D: [-5, infinity) R: (-infinity, 4]

• D: [-5, infinity) R: [4, -infinity)

• D: (-infinity, infinity) R: (-infinity, infinity)

• D: [4, infinity) R: (-infinity, -5]

Multiple Choice

The domain are the ______ values.

• y

• x

• Both x and y

Multiple Choice

The range are the _____ values.

• y

• x

• Both x and y

Multiple Choice

Find the domain for the function $$f\left(x\right)=\frac{2x-1}{3x+6}$$

• x cannot equal to 2

• x cannot equal to -2

• x cannot equal to 3

• All real numbers

Multiple Choice

Find the domain of the function $$f\left(x\right)=-\frac{2}{x+3}$$

• x cannot equal to 3

• x cannot equal to 1

• x cannot equal to -3

• All real numbers

Multiple Choice

Find the domain of the function. $$f\left(x\right)=\frac{x}{2x+4}$$

• x cannot equal to 2

• x cannot equal to 4

• x cannot equal to -2

• All real numbers

Multiple Choice

Find the domain of the function $$f\left(x\right)=\frac{x^3}{x+8}$$

• x cannot equal to 2

• x cannot equal to -2

• x cannot equal to -8

• All real numbers

Multiple Choice

What is the domain and range?

• D : All real number x ≠ -3
  R: All real number y≠ 1

• D : All real number x ≠ 1
  R: All real number y≠ -3

• D : All real number x ≠ 3
  R: All real number y≠ 1

• D : All real number x ≠ -1
  R: All real number y≠ 3