Question

1. write an equation that describes the function shown by the mapping diagrams below.

input, x: 2 4 6 8
output, y: 1 2 3 4

1. input, x: -55 -45 15 25 35

output, y: -65 -55 5 15 25

1. write a function rule for the statement, \the output is one half the input.\ then complete the table below.

Explanation:

Problem 6:

Step1: Analyze the input-output pairs

We have input \( x \) values: \( 2, 4, 6, 8 \) and output \( y \) values: \( 1, 2, 3, 4 \). Let's check the relationship. For \( x = 2 \), \( y = 1=\frac{2}{2} \); for \( x = 4 \), \( y = 2=\frac{4}{2} \); for \( x = 6 \), \( y = 3=\frac{6}{2} \); for \( x = 8 \), \( y = 4=\frac{8}{2} \). So the relationship is \( y=\frac{x}{2} \).

Step1: Analyze the input-output pairs

Input \( x \): \( -55, -45, 15, 25, 35 \); Output \( y \): \( -65, -55, 5, 15, 25 \). Let's find the difference: For \( x=-55 \), \( y = -65=-55 - 10 \); for \( x=-45 \), \( y=-55=-45 - 10 \); for \( x = 15 \), \( y = 5=15 - 10 \); for \( x = 25 \), \( y = 15=25 - 10 \); for \( x = 35 \), \( y = 25=35 - 10 \). So the relationship is \( y=x - 10 \).

Step1: Define the function rule

The output \( y \) is one half the input \( x \), so the function rule is \( y=\frac{1}{2}x \).

Step2: Complete the table (assuming the table has input values, let's say if input \( x = 10 \), \( y=\frac{10}{2}=5 \); if \( x = 12 \), \( y=\frac{12}{2}=6 \))

(Note: Since the table is partially visible, assuming common inputs, for \( x = 10 \), \( y = 5 \); for \( x = 12 \), \( y = 6 \))

Answer:

\( y = \frac{1}{2}x \)

Problem 7: