FIND RANGE OF A FUNCTION FROM THE GIVEN DOMAIN

Find the range for the functions with domain D :

Problem 1 :

D = {-1, 0, 2, 7, 9}, function: ‘add 3’.

Solution :

Let us create the function for the given rule.

f(x) = x + 3

D = {-1, 0, 2, 7, 9}

Range = {2, 3, 5, 10, 12}

Problem 2 :

D = {-2, -1, 0, 1, 2}, function: ‘square and then divide by 2’.

Solution :

Let us create the function for the given rule.

f(x) = x²/2

 D = {-2, -1, 0, 1, 2}

Range = {2, 1/2, 0, 1/2, 2}

Problem 3 :

D = {x | -2 < x < 2}, function: ‘multiply x by 2 then add 1’.

Solution :

f(x) = 2x + 1

D = {-1, 0, 1}

Range = {-1, 1, 3}

Problem 4 :

D = {x | -3 ≤ x ≤ 4}, function: ‘cube x’.

Solution :

f(x) = x³

D = {-3, -2, -1, 0, 1, 2, 3, 4}

If x = -3 ==> f(-3) = (-3)³  ==>  -27

If x = -2 ==> f(-2) = (-2)³  ==>  -8

If x = -1 ==> f(-1) = (-1)³  ==>  -1

If x = 0 ==> f(0) = (0)³  ==>  0

If x = 1 ==> f(1) = (1)³  ==>  1

If x = 2 ==> f(2) = 2³  ==>  8

If x = 3 ==> f(3) = 3³  ==>  27

If x = 4 ==> f(4) = 4³  ==>  64

Range = {-27, 8, -1, 0, 1, 8, 27, 64}

Problem 2 :

For the domain {0, 1, 2, 3} and the function ‘subtract 2’, find the range.

Solution :

f(x) = x - 2

D = {0, 1, 2, 3}

If x = 0 ==> f(0) = 0 - 2  ==>  -2

If x = 1 ==> f(1) = 1 - 2  ==>  -1

If x = 2 ==> f(2) = 2 - 2  ==>  0

If x = 3 ==> f(3) = 3 - 2  ==>  1

Range = {-2, -1, 0, 1}