Question

How do you find the domain and range of \[y = 2\left| {x - 3} \right| + 5\] ?

Answer 1

Hint: We should know about the following term
Domain: The domain is the set of all possible x-values which will make the function “work”, and will output real y-values.
Range: The range of a function is the set of all output values (y-values).

Complete step by step solution:
As we have to find the domain and range of given function,
 \[y = 2\left| {x - 3} \right| + 5\]
Let compare it with $y = a\left| {x - b} \right| + c$
As we know the domain is set of all possible values of $x$ that mean whatever we can put in place of $x$ whose output will be real value.
As we notice there. We find that we can put any value of $x$ in this place so we will get the real value of $y$ .
It’s Domain will be all real number or $( - \infty ,\infty )$
Range for a function will depend upon the value of \[y\] which we get after putting the value of $x$ . As domain is $( - \infty ,\infty )$ .
\[y\] will always be zero or greater than $5$ as terms inside the modules always be zero or greater than zero.
So, range of \[y\] will be $[5,\infty )$

Note: Function in mathematics is used as an expression, rule or law that defines a relationship between one variable (the independent variable) and another (the dependent). Functions are ubiquitous in mathematics and essential for formulating physical relationships in science.