Question

the function $g(x)$ is graphed below. rewrite the points on the graph in table and using function notation. your xs should be in order from least to greatest.
table

$x$	$g(x)$

function notation $g(x)=y$

Explanation:

Step1: Identify the coordinates of each point on the graph.

Looking at the graph, the blue dots are at:

• When \( x = -4 \), \( y = 3 \) (since the point is at (-4, 3))
• When \( x = -3 \), \( y = 2 \) (point at (-3, 2))
• When \( x = -1 \), \( y = 0 \) (point at (-1, 0))
• When \( x = 2 \), \( y = -3 \) (point at (2, -3))
• When \( x = 4 \), \( y = -5 \) (point at (4, -5))

Step2: Order the x-values from least to greatest.

The x-values are -4, -3, -1, 2, 4 (in order from least to greatest).

Step3: Create the table.

For each x-value, find the corresponding \( g(x) \) (which is y).

• For \( x = -4 \), \( g(-4) = 3 \)
• For \( x = -3 \), \( g(-3) = 2 \)
• For \( x = -1 \), \( g(-1) = 0 \)
• For \( x = 2 \), \( g(2) = -3 \)
• For \( x = 4 \), \( g(4) = -5 \)

Step4: Write the function notation.

Using \( g(x) = y \), we have:

• \( g(-4) = 3 \)
• \( g(-3) = 2 \)
• \( g(-1) = 0 \)
• \( g(2) = -3 \)
• \( g(4) = -5 \)

Table:

\( x \)	\( g(x) \)
-3	2
-1	0
2	-3
4	-5

Function Notation:

\( g(-4) = 3 \)
\( g(-3) = 2 \)
\( g(-1) = 0 \)
\( g(2) = -3 \)
\( g(4) = -5 \)

Answer:

Table:

\( x \)	\( g(x) \)
-3	2
-1	0
2	-3
4	-5

Function Notation:

\( g(-4) = 3 \), \( g(-3) = 2 \), \( g(-1) = 0 \), \( g(2) = -3 \), \( g(4) = -5 \)