The problem defines a function $P$ that represents the perimeter of a square with side length $x$. The problem asks us to complete a table of values for $P(x)$ given $x$, write an equation for $P(x)$, and sketch a graph of $P(x)$.

1. Problem Description

The problem defines a function $P$ that represents the perimeter of a square with side length $x$. The problem asks us to complete a table of values for $P(x)$ given $x$, write an equation for $P(x)$, and sketch a graph of $P(x)$.

2. Solution Steps

a. Completing the table:

The perimeter of a square is given by $P = 4s$, where $s$ is the side length. In this case, the side length is $x$, so $P(x) = 4x$. We need to calculate $P(x)$ for $x = 0, 1, 2, 3, 4, 5, 6$.

$P(0) = 4(0) = 0$

$P(1) = 4(1) = 4$

$P(2) = 4(2) = 8$

$P(3) = 4(3) = 12$

$P(4) = 4(4) = 16$

$P(5) = 4(5) = 20$

$P(6) = 4(6) = 24$

b. Writing an equation to represent function $P$:

As explained above, the equation for the perimeter of a square with side length $x$ is $P(x) = 4x$.

c. Sketching a graph of function $P$:

We can plot the points from the completed table on the provided graph. The points are $(0, 0), (1, 4), (2, 8), (3, 12), (4, 16), (5, 20), (6, 24)$. These points lie on a straight line.

3. Final Answer

a. Completed table:

x | 0 | 1 | 2 | 3 | 4 | 5 | 6

---|---|---|---|---|---|---|---

P(x) | 0 | 4 | 8 | 12 | 16 | 20 | 24

b. Equation for function $P$:

$P(x) = 4x$

c. Graph:

Plot the points (0,0), (1,4), (2,8), (3,12), (4,16), (5,20), (6,24) and draw a line through these points. Since I cannot directly draw a graph, I will describe it. The graph is a straight line passing through the origin with a slope of

4. For every increase of 1 in the x-direction (side length), the perimeter increases by 4 in the y-direction. The line extends from (0,0) to (6,24) in the range shown on the graph.