Question

Match each function to its domain and range.

domain: {0, 1, 3, 5, 6}
range: {-20, -16, -8, 0, 4}

domain: {-2, -1, 0, 3, 4}
range: {-13, -8, -3, 12, 17}

domain: {-4, -2, 0, 2, 4}
range: {-40, -20, 0, 20, 40}

domain: {-3, -2, -1, 2, 6}
range: {0.5, 0, -1.5, 3, 2}


f (x) = 4 - 4x

f (x) = 5x - 3

f (x) = -10x

f (x) = 3/x + 1.5

Answer 1

The function: f(x) = 4 - 4x has the domain and range

domain: {0, 1, 3, 5, 6}

range: {-20, -16, -8, 0, 4}

The function: f(x) = 5x - 3 has the domain and range

domain: {-2, -1, 0, 3, 4}

range: {-13, -8, -3, 12, 17}

The function: f(x) = -10x has the domain and range

domain: {-4, -2, 0, 2, 4}

range: {-40, -20, 0, 20, 40}

The function: f(x)=3/x+1.5 has the domain and range

domain: {-3, -2, -1, 2, 6}

range: {0.5, 0, -1.5, 3, 2}

Answer 2

The domain of a function is the set of the possible values of x, while the range of a function is the set of the resulting values of the functions from the domain.

By inspection it can be seen that the function
f(x) = 4 - 4x has the domain and range as follows:
domain: {0, 1, 3, 5, 6}
range: {-20, -16, -8, 0, 4}

i.e. 4 - 4(0) = 4 - 0 = 4
4 - 4(1) = 4 - 4 = 0
4 - 4(3) = 4 - 12 = -8
4 - 4(5) = 4 - 20 = -16
4 - 4(6) = 4 - 24 = -20


Also, the function
f(x) = 5x - 3 has the domain and range as follows:
domain: {-2, -1, 0, 3, 4}
range: {-13, -8, -3, 12, 17}

i.e. 5(-2) - 3 = -10 - 3 = -13
5(-1) - 3 = -5 - 3 = -8
5(0) - 3 = 0 - 3 = -3
5(3) - 3 = 15 - 3 = 12
5(4) - 3 = 20 - 3 = 17


Also, the function
f(x) = -10x has the domain and range as follows:
domain: {-4, -2, 0, 2, 4}
range: {-40, -20, 0, 20, 40}

i.e. -10(-4) = 40
-10(-2) = 20
-10(0) = 0
-10(2) = -20
-10(4) = -40

Also, the function

`f(x)=(3)/(x)+1.5` has the domain and range as follows:
domain: {-3, -2, -1, 2, 6}
range: {0.5, 0, -1.5, 3, 2}

i.e.

`(3)/(-3)+1.5=-1+1.5=0.5 \\ \\ (3)/(-2)+1.5=-1.5+1.5=0 \\ \\ (3)/(-1)+1.5=-3+1.5=-1.5 \\ \\ (3)/(2)+1.5=1.5+1.5=3 \\ \\ (3)/(6)+1.5=0.5+1.5=2`