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In this lesson, we will learn how to find the domain and range of a rational function either from its graph or its defining rule.

Q1:

Find the value of π given π ( π₯ ) = 1 4 2 5 π₯ + 6 0 π₯ + 3 6 2 where π ( π ) is undefined.

Q2:

Determine the domain and the range of the function π ( π₯ ) = 1 π₯ β 2 .

Q3:

Simplify the function π ( π₯ ) = π₯ + 7 π₯ β 8 π₯ π₯ β 6 5 π₯ + 6 4 3 2 4 2 , and find its domain.

Q4:

Find the domain of the function π ( π₯ ) = π₯ + 4 ( π₯ β 8 ) 2 .

Q5:

The domain of an algebraic fractional function is the set of all real numbers except the .

Q6:

Determine the domain and the range of the function π ( π₯ ) = π₯ β 1 6 π₯ + 4 2 .

Q7:

Define a function on real numbers by π ( π₯ ) = 2 π₯ + 3 4 π₯ + 5 .

What is the domain of this function?

Find the one value that π ( π₯ ) cannot take.

What is the range of this function?

Q8:

Given that the domain of the function π ( π₯ ) = 3 6 π₯ + 2 0 π₯ + π is β β { β 2 , 0 } , evaluate π ( 3 ) .

Q9:

Determine the domain and the range of the function π ( π₯ ) = 1 | π₯ β 2 | .

Q10:

Identify the domain of .

Q11:

Determine the domain of the function π ( π₯ ) = 4 π₯ + 3 π₯ 6 π₯ + 7 π₯ 2 2 .

Q12:

For which values of π₯ is the function π ( π₯ ) = π₯ β 2 5 π₯ β 1 2 π₯ + 3 2 2 2 not defined?

Q13:

If the common domain of the two functions π ( π₯ ) = 3 π₯ + 3 1 and π ( π₯ ) = 3 π₯ π₯ β π 2 is β β { β 3 , 4 } , what is the value of π ?

Q14:

The function π ( π₯ ) = π₯ β 2 π₯ β 1 has an additive inverse if the domain is .

Q15:

If the function π ( π₯ ) = π₯ + 3 π₯ β 9 , what is the domain of its multiplicative inverse?

Q16:

Determine the domain and the range of the function .

Q17:

Determine the domain and the range of π ( π₯ ) = π₯ β 4 π₯ β 2 2 .

Q18:

Determine the domain of the function π ( π₯ ) = π₯ + 3 | π₯ β 1 | + 7 2 .

Q19:

Given the function π ( π₯ ) = π₯ + 8 π₯ ( π₯ + 8 ) ( π₯ + 5 ) 2 2 , find the multiplicative inverse of π in its simplest form and state its domain.

Q20:

Determine the domain of the function π ( π₯ ) = | π₯ β 1 | | π₯ | β 8 .

Q21:

Determine the domain and the range of the function π ( π₯ ) = π₯ + 9 π₯ + 2 0 π₯ + 5 2 .

Q22:

Determine the domain and the range of the function π ( π₯ ) = β 1 0 π₯ + 6 4 0 π₯ β 6 4 2 2 .

Q23:

Determine the domain and the range of the function π ( π₯ ) = β 5 π₯ β 1 5 π₯ + 3 .

Q24:

Given that the domain of the function π ( π₯ ) = 8 π₯ β 9 1 is the same as the domain of the function π ( π₯ ) = π₯ β 5 π₯ + π 2 , what is the value of π ?

Q25:

Determine the domain and the range of the function π ( π₯ ) = π₯ + 2 π₯ β 8 π₯ + 4 2 .

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