Algebra - Graphing Functions

Section 3.5 : Graphing Functions

2. Construct a table of at least 4 ordered pairs of points on the graph of the following function and use the ordered pairs from the table to sketch the graph of the function.

\[f\left( x \right) = \sqrt {x + 1} \]

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For this function we’ll use points that give function values that are integers to make the graphing a little easier.

Here is the table of points we’ll use for this problem.

$x$	$f\left( x \right)$	$\left( {x,y} \right)$
-1	0	$\left( { - 1,0} \right)$
0	1	$\left( {0,1} \right)$
3	2	$\left( {3,2} \right)$
8	3	$\left( {8,3} \right)$

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Here is a sketch of the function.

$The graph of $f\left( x \right) = \sqrt {x + 1} $. It starts at $\left( { - 1,0} \right)$ and increases as it moves to the right, rising steeply at first and then flattening out. The points from the table are marked and labeled on the graph and they are $\left( { - 1,0} \right)$, $\left( {0,1} \right)$, $\left( {3,2} \right)$ and $\left( {8,3} \right)$.$

\(x\)	\(f\left( x \right)\)	\(\left( {x,y} \right)\)
-1	0	\(\left( { - 1,0} \right)\)
0	1	\(\left( {0,1} \right)\)
3	2	\(\left( {3,2} \right)\)
8	3	\(\left( {8,3} \right)\)