Question

Match each function to its domain and range.

Answer 1

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

i.e.
$\frac{3}{-3}+1.5=-1+1.5=0.5 \\ \\ \frac{3}{-2}+1.5=-1.5+1.5=0 \\ \\ \frac{3}{-1}+1.5=-3+1.5=-1.5 \\ \\ \frac{3}{2}+1.5=1.5+1.5=3 \\ \\ \frac{3}{6}+1.5=0.5+1.5=2$