Question

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.

\({\bf{y = }}\frac{{\bf{1}}}{{{\bf{x + 2}}}}\)

Short answer

The graph of \(y = \frac{1}{{x + 2}}\) can be obtained by shifting the graph of \(\frac{1}{x}\)by 2 units to the left.

Step-by-step solution

Given Data

The given function is \(y = \frac{1}{{x + 2}}\)

Solution

We have to draw the graph of\(y = \frac{1}{{x + 2}}.\)

Let the standard function be;

\(f\left( x \right) = \frac{1}{x}\)

The graph of\(f\left( {x + c} \right)\)can be obtained by shifting the graph of\(f\left( x \right)\)by 2 units to the left.

Therefore the graph of\(y = \frac{1}{{x + 2}}\)can be obtained by shifting the graph of\(\frac{1}{x}\)horizontally by 2 units to the left.

Therefore, the required graph of \(y = \frac{1}{{x + 2}}\) is given below;