Question

Find the domain and sketch the graph of the functions\({\bf{F}}\left( {\bf{x}} \right){\bf{ = }}\left| {{\bf{2x + 1}}} \right|\).

Short answer

The domain of the function \({\bf{F}}\left( {\bf{x}} \right){\bf{ = }}\left| {{\bf{2x + 1}}} \right|\) is\(\left( { - \infty , + \infty } \right)\)and the graph of the function is given in figure (1).

Step-by-step solution

Determine the domain of the function

The domain of a function is the set of all possible input values.

The given function is\(F\left( x \right) = |2x + 1|\).

The given function is defined for all real values of\(x\).

Therefore, the domain of the function \(F\left( x \right) = |2x + 1|\)is\(\left( { - \infty , + \infty } \right)\).

Sketch the graph of the function

The intersection points of the graph on the x and y axis are calculated as:

For \(x = 0\)

\(\begin{aligned}F\left( x \right) &= \left| {2\left( 0 \right) + 1} \right|\\F\left( x \right) &= 1\end{aligned}\)

The graph passes through the\(y - \)axis at\(\left( {0,1} \right)\).

For \(F\left( x \right) = 0\)

\(\begin{aligned}0 &= \left| {2x + 1} \right|\\x &= - 0.5\end{aligned}\)

The graph passes through the\(x - \)axis at\(\left( { - 0.5,0} \right)\).

Therefore, the graph of the function is given below as:

Figure (1)

Therefore, the graph of the function is given in figure (1).