Question

How do you find the range of $y=3x-5$: given domain =\left\\{ 0,1,2,3 \right\\}?

Answer 1

As we know that Domain is plotted on X-axis it means the domain represents the values of x in the given equation. Range is plotted on the Y-axis, so to find the values of y we will put the different values of x in the equation given in the question and get the desired answer.

Complete step by step answer:
We have been given that domain of $y=3x-5$ is \left\\{ 0,1,2,3 \right\\}.
We have to find the range of $y=3x-5$.
Now, we know that Domain is the number that we give to the function. Domain represents the x values in the equation.
To find the range i.e. y values we need to substitute the given x values in the equation one by one.
Let us first substitute the value $x=0$ in the given equation. Then we will get
$\begin{aligned} & \Rightarrow y=3\times 0-5 \\\ & \Rightarrow y=0-5 \\\ & \Rightarrow y=-5 \\\ \end{aligned}$
Let us substitute the value $x=1$ in the given equation. Then we will get
$\begin{aligned} & \Rightarrow y=3\times 1-5 \\\ & \Rightarrow y=3-5 \\\ & \Rightarrow y=-2 \\\ \end{aligned}$
Let us substitute the value $x=2$ in the given equation. Then we will get
$\begin{aligned} & \Rightarrow y=3\times 2-5 \\\ & \Rightarrow y=6-5 \\\ & \Rightarrow y=1 \\\ \end{aligned}$
Let us substitute the value $x=3$ in the given equation. Then we will get
$\begin{aligned} & \Rightarrow y=3\times 3-5 \\\ & \Rightarrow y=9-5 \\\ & \Rightarrow y=4 \\\ \end{aligned}$

Hence we get the range of $y=3x-5$ as \left\\{ -5,-2,1,4 \right\\}

Note: Domain and range is usually denoted using interval notation. As Domain is numbers that we give to the function whereas range is numbers the function gives back to us. The point to note is that domain and range are always written from smaller to larger values. For this question if we write the range as \left\\{ 1,4,-5,-2 \right\\}, then it is incorrect.