Question

Graph the function f(x)=|x|+3 .State the domain and range .​

Answer 1

Answer:

Domain is all real numbers. Range is $[3,\infty)$

Step-by-step explanation:

The function $f(x)=|x|+3$ is a transformation of the parent function $f(x)=|x|$ by moving the function up by 3 units.

So, the graph of the function is shown below.

From the graph, it is clear that the $x$ values has no limitation and hence can take any real values. Domain is the set of all possible $x$ values.

So, domain is the set of all real numbers.

Range is the set of all possible values for $y$ for the given domain.

From the graph, the minimum value of $y$ is at the point ($(0,3)$. So, the minimum value of y is 3. The $y$ value then goes on increasing towards infinity.

Therefore, range is a real number greater than or equal to 3.

So, range is $y\geq 3$ or  $[3,\infty)$