Graph the given square root functions, f and g, in the same...

Graph the given square root functions, $f$ and $g,$ in the same rectangular coordinate system. Use the integer values of $x$ given to the right of each function to obtain ordered pairs. Because only nonnegative numbers have square roots that are real numbers, be sure that each graph appears only for values of $x$ that cause the expression under the radical sign to be greater than or equal to zero. Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$. $$ \begin{aligned} &f(x)=\sqrt{x} \quad(x=0,1,4,9) \text { and }\\ &g(x)=\sqrt{x}-1 \quad(x=0,1,4,9) \end{aligned} $$

Graph the given square root functions, $f$ and $g,$ in the same rectangular coordinate system. Use the integer values of $x$ given to the right of each function to obtain ordered pairs. Because only nonnegative numbers have square roots that are real numbers, be sure that each graph appears only for values of $x$ that cause the expression under the radical sign to be greater than or equal to zero. Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$.
$$
\begin{aligned}
&f(x)=\sqrt{x} \quad(x=0,1,4,9) \text { and }\\
&g(x)=\sqrt{x}-1 \quad(x=0,1,4,9)
\end{aligned}
$$

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Key Concepts

Function Transformation

Function transformation refers to modifications that alter a function’s graph. A vertical shift, such as subtracting one from a function, moves the entire graph down or up without changing its overall shape, making it easier to compare related functions.

Graphing with Ordered Pairs

Graphing by using ordered pairs involves calculating the function's value at given x-values and plotting the resulting points on a coordinate plane. This method helps visualize the curve of the function and ensures accuracy by relying on specific, computed coordinates.

Domain Restrictions

In square root functions, the domain is limited to values that make the expression inside the radical greater than or equal to zero. This restriction is essential because the square root of a negative number is not a real number, which confines the graph to a specific portion of the coordinate plane.

Square Root Function

The square root function takes a nonnegative number and returns its principal (nonnegative) square root. This function is defined only for values where the expression inside the square root (the radicand) is nonnegative, and it produces a graph that starts at the origin and increases gradually.

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