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In this lesson, we will learn how to identify the domain and range of functions from schematics, graphs, and equations.

Q1:

Determine the range of π ( π₯ ) .

Q2:

Using the figure below, determine the range of π ( π₯ ) .

Q3:

Given that π βΆ π β π , π = { β 9 , β 6 , β 5 } , π = { 3 , 4 , 6 , 9 } , and π = { ( β 9 , 4 ) , ( β 6 , 4 ) , ( β 5 , 9 ) } , which of the following sets correctly specify the range of the function?

Q4:

If π βΆ [ 2 , 2 1 ] βΆ β , where π ( π₯ ) = 3 π₯ β 1 0 , find the range of π .

Q5:

Find the domain of the function π ( π₯ ) = β π₯ .

Q6:

Find the domain of the function π ( π₯ ) = β 3 β 2 π₯ β 1 .

Q7:

The figure below shows the graph of a function .

What is the range of the function?

Q8:

Determine the domain of the function

Q9:

Determine the range of the function

Q10:

Determine the range of the function in the given figure.

Q11:

Determine the domain of the function represented in the graph below.

Q12:

Find the range of the function

Q13:

Determine the domain of the function π ( π₯ ) = β | π₯ | β 3 3 .

Q14:

Determine the domain of the function π ( π₯ ) = β π₯ + 3 β β 8 β π₯ .

Q15:

Determine the domain of the function π ( π₯ ) = 1 | π₯ | β 6 5 .

Q16:

Determine the range of the function represented in the figure below.

Q17:

Determine the range of the function represented by the figure in π .

Q18:

Given the function π = { ( 2 , 1 ) , ( 1 , 3 ) , ( 3 , β 1 ) , ( 7 , 3 ) } , answer the following.

Evaluate π ( 2 ) .

Evaluate π ( 3 ) .

Evaluate π ( 0 ) .

What is the domain of π ?

What is the range of π ?

Solve π ( π₯ ) = 3 .

What is the solution set of π ( π₯ ) = β 1 ?

What is the solution set of π ( π₯ ) = 0 ?

Q19:

Determine the domain and the range of the function π ( π₯ ) = β 6 ( π₯ + 9 ) + 8 3 .

Q20:

Functions π and π have the same domain {1, 2, 3, 4}. Which of the following statements must be true?

Q21:

What is the range of the function π ( π₯ ) = π₯ + 1 2 on the domain β€ (which is the domain of all of the integers)?

Q22:

If π βΆ { β 4 , β 1 , 4 , β 2 } β [ 6 , 2 5 ] and π ( π₯ ) = π₯ + 5 2 , find the range of π .

Q23:

If , where , find the range of .

Q24:

Given that π = { π₯ βΆ π₯ β β€ , β 9 β€ π₯ β€ 1 0 } and π π β β : , where the graph of the function can be represented by πΊ = { ( 1 0 , 1 ) , ( β 7 , β 1 ) , ( β 4 , β 1 0 ) , ( β 1 , β 1 0 ) , ( β 9 , 0 ) } π , determine its range.

Q25:

π = { 1 4 , 7 , 1 1 } , π = { 3 3 , 1 , 4 2 , 1 2 , 2 1 } , and π is a relation from π to π , where π π π means that π = 1 3 π for each π β π and π β π . Determine the relation π , state whether it represents a function or not, and write its range if it is a function.

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