Question

1 match each equation with a description of the function it represents.
a ( f(x) = 2x + 4 )
1 to get the output, add 4 to the input, then multiply the result by 2.
b ( g(x) = 2(x + 4) )
2 to get the output, add 2 to the input, then multiply the result by 4.
c ( h(x) = 4x + 2 )
3 to get the output, multiply the input by 2, then add 4 to the result.
d ( k(x) = 4(x + 2) )
4 to get the output, multiply the input by 4, then add 2 to the result.
2 function ( p ) represents the perimeter, in inches, of a square with side length ( x ) inches.
a. complete the table.

( x )	0	1	2	3	4	5	6
( p(x) )

b. write an equation to represent function ( p ).
c. sketch a graph of function ( p ).
graph with x-axis labeled side length (inches) from 0 to 8, y-axis labeled perimeter (inches) from 0 to 24, grid lines, and origin at (0,0)

Explanation:

Problem 1: Matching Functions with Descriptions

for Each Match:

• For \( F(x) = 2x + 4 \): The operation is multiply input by 2, then add 4. So matches with description 3.
• For \( g(x) = 2(x + 4) \): The operation is add 4 to input, then multiply by 2. So matches with description 1.
• For \( h(x) = 4x + 2 \): The operation is multiply input by 4, then add 2. So matches with description 4.
• For \( k(x) = 4(x + 2) \): The operation is add 2 to input, then multiply by 4. So matches with description 2.

Answer:

for Problem 1:

• A - 3
• B - 1
• C - 4
• D - 2

Problem 2: Perimeter of a Square

Part (a): Completing the Table

The perimeter of a square is given by \( P = 4 \times \text{side length} \), so \( P(x) = 4x \).

• For \( x = 0 \): \( P(0) = 4(0) = 0 \)
• For \( x = 1 \): \( P(1) = 4(1) = 4 \)
• For \( x = 2 \): \( P(2) = 4(2) = 8 \)
• For \( x = 3 \): \( P(3) = 4(3) = 12 \)
• For \( x = 4 \): \( P(4) = 4(4) = 16 \)
• For \( x = 5 \): \( P(5) = 4(5) = 20 \)
• For \( x = 6 \): \( P(6) = 4(6) = 24 \)

The table becomes:

\( x \)	0	1	2	3	4	5	6

Part (b): Equation for Function \( P \)

The perimeter of a square with side length \( x \) is \( 4 \) times the side length. So the equation is \( P(x) = 4x \).

Part (c): Sketching the Graph

The function \( P(x) = 4x \) is a linear function. To sketch the graph:

• Plot the points from the table: (0, 0), (1, 4), (2, 8), (3, 12), (4, 16), (5, 20), (6, 24).
• Draw a straight line passing through these points. The line will have a slope of 4 and pass through the origin.

Final Answers:

Problem 1:

A - 3, B - 1, C - 4, D - 2

Problem 2:

a.

\( x \)	0	1	2	3	4	5	6

b. \( P(x) = 4x \)

c. (Graph with points (0,0), (1,4), (2,8), etc., connected by a straight line)