# How do you find the range of y = z^2 - 3z; given Domain = {-1, 0, 1, 2}?

Sep 8, 2016

$\text{The Range=} \left\{4 , 0 , - 2\right\}$.

#### Explanation:

$y = {z}^{2} - 3 z \text{, and, let } D = \left\{- 1 , 0 , 1 , 2\right\}$.

By, Range of the given function, we mean, the Set of all values of

$y$, to be determined by using the values of $z$ choosing from the

given Domain Set, here, $D$.

Thus, in Notation, the Range$= \left\{y = {z}^{2} - 3 z : z \in D\right\}$.

Now, $z = - 1 \Rightarrow y = {z}^{2} - 3 z = {\left(- 1\right)}^{2} - 3 \left(- 1\right) = 1 + 3 = 4$

$z = 0 \Rightarrow y = 0$

$z = 1 \Rightarrow y = - 2$

$z = 2 \Rightarrow y = - 2$

Therefore, $\text{The Range=} \left\{4 , 0 , - 2\right\}$.