Question

3 - 48. use your pattern skills to copy and complete the table below. homework help

in (x)	2	10	6	7	-3		-10	100	x
out (y)	2	6	4			15

a. explain in words what is done to the input value, x, to produce the output value, y.
b. write the process you described in part (a) in algebraic symbols.

Explanation:

Step1: Analyze known pairs

For \(x = 2\), \(y=2\); for \(x = 10\), \(y = 6\); for \(x=6\), \(y = 4\). Notice that \(y=x - 0\) when \(x = 2\), \(y=x - 4\) when \(x = 10\), \(y=x - 2\) when \(x = 6\). The pattern seems to be \(y=x - (x\bmod2)\).

Step2: Fill in the table

When \(x = 7\), \(y=7-(7\bmod2)=7 - 1=6\).
When \(x=-3\), \(y=-3-(-3\bmod2)=-3 - 1=-4\).
Let the missing \(x\) - value be \(a\). If \(y = 15\), then \(15=a-(a\bmod2)\). Since \(15\) is odd, \(a\) must be even and \(a=15\).
When \(x=-10\), \(y=-10-(-10\bmod2)=-10-0=-10\).
When \(x = 100\), \(y=100-(100\bmod2)=100 - 0=100\).
When \(x=x\), \(y=x-(x\bmod2)\).

Step3: Answer part (a)

Subtract the remainder when the input is divided by 2 from the input.

Step4: Answer part (b)

\(y=x-(x\bmod2)\)

Answer:

a. Subtract the remainder when the input is divided by 2 from the input.
b. \(y=x-(x\bmod2)\)

IN (\(x\))	2	10	6	7	-3	15	-10	100	\(x\)