 # Graph the function by hand, not by plotting points, but hexacordoK 2021-08-14 Answered
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.
$$\displaystyle{y}={2}\sqrt{{{x}+{1}}}$$

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We will start with the graph of the standard/parent function $$\displaystyle{y}=\sqrt{{x}}$$
The graph of $$y=k \cdot f(x)$$ is obtained by vertically stretching the graph of $$y = f(x)$$ by a factor of k.
Therefore, if we vertically stretch the graph of $$\displaystyle{y}=\sqrt{{x}}$$ by a factor of 2, we will get the graph of $$\displaystyle{y}={2}\sqrt{{x}}$$
In the graph below:
The blue dashed curve represents $$\displaystyle{y}=\sqrt{{x}}$$
The red solid curve represents $$\displaystyle{y}={2}\sqrt{x}$$ 