Question

How do you find the domain and range of $h(x) = 3x + 9$ ?

Answer 1

We are given a function and we have to find its domain and range. Domain is the value of X. It is the input values of that can be used in a function and range is the output values of the function. The function we are given is the equation of line. Hence the domain and range of the equation of lines have no restrictions and include all real numbers. By using this concept we will find the domain and range of the given equation.

Complete step-by-step solution:
Step1: We are given a function which is an equation of line i.e. $h(x) = 3x + 9$ and we have to find its domain and range. Since it is an equation of line domain and range will have no restrictions and include all real numbers.
Step2: For the values of the domain we can input any value of real numbers. For domain h(x) = \left\\{ {x|x \in R} \right\\} or in an interval notation of $\left( { - \infty ,\infty } \right)$ the given equation will accept all values. And doesn’t make the function undefined at any point.
Step3: For the values of range we can get any value of real number as an output. For range \left\\{ {h(x)|h(x) \in R} \right\\} or in interval notation $\left( { - \infty ,\infty } \right)$ .

Hence the domain is \left\\{ {x \in \left( { - \infty ,\infty } \right)} \right\\} and range is \left\\{ {h(x) \in \left( { - \infty ,\infty } \right)} \right\\}

Note: In such types of questions students are mainly confused between domain and range so they should know the difference between them. The domain is the input values of the variable and range is the output value of the function. The given equation is a simple equation which is true for all real numbers. But sometimes some functions have some restrictions both in domain and range.