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.

\(y = 1 - 2\sqrt {x + 3} \)

Short answer

The plot of the function \(y = 1 - 2\sqrt {x + 3} \) is:

Step-by-step solution

Given data

The function to be plotted is\(y = 1 - 2\sqrt {x + 3} \).

Plot of the function \(y = \sqrt x \)

The plot of the function \(y = \sqrt x \) is as follows

Figure 1

Step 3:Plot of the function \(y = 1 - 2\sqrt {x + 3} \)

The plot of the function\(y = \sqrt {x + 3} \)can be obtained by shifting Figure 1to the left by 3 units as follows

Figure2

The plot of the function \(y = - \sqrt {x + 3} \)can be obtained by taking the reflection of Figure 2 about \(x\) axis and remains the same as Figure 2.

The plot of the function \(y = 1 - \sqrt {x + 3} \)can be obtained by shifting Figure 2 by 1 unit upwards as follows: