FINDING THE DOMAIN AND RANGE OF A FUNCTION FROM A GRAPH

Find the Domain and Range for each graph.

Problem 1 :

Solution:

In the graph above, x- coordinates are all the integers from -∞ to 5 and the y- coordinates are all the integers from -∞ to 2.

Domain = {x ∈ R | -∞ < x ≤ 5}

Range = {y ∈ R | -∞ < y ≤ 2}

Problem 2 :

Solution:

In the graph above, x- coordinates are all the integers from -5 to -2 and the y- coordinates are all the integers from -4 to 4.

Domain = {x ∈ R | -5 < x < -2}

Range = {y ∈ R | -4 < y < 4}

Problem 3 :

Solution:

In the graph above, x- coordinates are all the integers from -4 to ∞ and the y- coordinates are all the integers from -1 to ∞.

Domain = {x ∈ R | -4 < x < ∞}

Range = {y ∈ R | -1 < y < ∞}

Problem 4 :

Solution:

In the graph above, x- coordinates are all the integers from -∞ to 3 and the y- coordinates are all the integers from -2 to ∞.

Domain = {x ∈ R | -∞ < x ≤ 3}

Range = {y ∈ R | -2 ≤ y < ∞}

Problem 5 :

Solution:

In the graph above, x- coordinates are all the integers from -4 to 3 and the y- coordinates are all the integers from -5 to 2.

Domain = {x ∈ R | -4 < x ≤ 3}

Range = {y ∈ R | -5 < y ≤ 2}

Problem 6 :

Solution:

In the graph above, x- coordinates are all the integers from -4 to ∞ and the y- coordinates are all the integers from 0 to ∞.

Domain = {x ∈ R | -4 ≤ x < ∞}

Range = {y ∈ R | 0 ≤ y < ∞}

Problem 7 :

Solution:

In the graph above, x- coordinates are all the integers from -5 to 4 and the y- coordinates are all the integers from -3 to 3.

Domain = {x ∈ R | -5 ≤ x ≤ 4}

Range = {y ∈ R | -3 ≤ y ≤ 3}

Problem 8 :

Solution:

In the graph above, x- coordinates are all the integers from -∞ to 0 and the y- coordinates are all the integers from -3 to ∞.

Domain = {x ∈ R | -∞ < x ≤ 0}

Range = {y ∈ R | -3 ≤ y < ∞}

Problem 9 :

Solution:

In the graph above, x- coordinates are all the integers from -∞ to ∞ and the y- coordinates are all the integers from -∞ to ∞.

Domain = {x ∈ R | -∞ < x < ∞}

Range = {y ∈ R | -∞ < y < ∞}