Q50. - Algebra 2

Question

Graph The function $h\left(x\right)=\left|x-3\right|$and identify the domain and range of the function $h\left(x\right)=\left|x-3\right|$.

Step-by-Step Solution

Answer

The graph of the inequality is

Domain is $\left(-\infty ,\infty \right)$

Range is $\left[0,\infty \right)$

Step-1 – Apply the concept of plotting graph and finding domain and range of the function.

Graph of the function can be drawn by putting the value in the equation and it can be plot by Desmos graphing calculator where we have to put the value of the function and domain and range can find using the graph the value of $x$is domain and value of $y$is range.

Step-2 – Plot the graph of the given function

The graph can be plot as

Step-3 – Describe the Domain and range of the function

Here From the graph it’s cleared that the domain is $\left(-\infty ,\infty \right)$

As, the blue line is moving from $-\infty$to $\infty$as shown in the graph.

Whereas Range is $\left[0,\infty \right)$, because the graph can take any value greater than or equal to 0.