Question

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

Answer 1

To find the domain, we need to look at the values of the independent variables which are allowed to use as explained above, i.e., no zero at the bottom of fraction and no negative sign inside the square root.
The set of all the outputs of a function is known as the range of the function or after substituting the domain, the entire set of all values possible as outcomes of the dependent variable.

Complete Step by Step Solution:
It is given that the question stated as $h(x) = 3x + 9$
We have to find the domain and range of $h(x) = 3x + 9$.
Now, we have to take $h(x) = 3x + 9$ is the equation of a line, the domain and range of all lines have no restrictions and include all real numbers.
So, domain $\\{ x\left| x \right. \in \Re \\}$ or in interval notation $( - \infty ,\infty )$
And, range $\\{ h(x)\left| {h(x)} \right. \in \Re \\}$ or in interval notation $( - \infty ,\infty )$
Hence, the domain $\\{ x\left| x \right. \in \Re \\}$ or in interval notation $( - \infty ,\infty )$and range $\\{ h(x)\left| {h(x)} \right. \in \Re \\}$ or in interval notation $( - \infty ,\infty )$
Hence, we got the required answer.

Note: The set of all possible values which qualify as inputs to a function is known as the domain of the function, or it can also be defined as the entire set of values possible for independent variables.
The domain can be found in – the denominator of the fraction is not equal to zero and the digit under the square root bracket is positive.
The set of all the outputs of a function is known as the range of the function or after substituting the domain, the entire set of all values possible as outcomes of the dependent variable.