# Spectrum Math Grade 8 Chapter 4 Lesson 2 Answer Key Input/Output Tables

Students can use the Spectrum Math Grade 8 Answer Key Chapter 4 Lesson 4.2 Input/Output TablesĀ as a quick guide to resolve any of their doubts.

## Spectrum Math Grade 8 Chapter 4 Lesson 4.2 Input/Output Tables Answers Key

In a function, each value of x relates to only one value of y. For example, if y = x + 6, whatever x is, y must be greater than x by the number 6.
A function table shows the values for each pair of variables as the result of the particular function.

Complete each function table for the given function.

Question 1.
a.
y = x + 6

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
out put = input + 6
y = x + 6
y = x + 6 = -10 + 6 = -4
y = x + 6 = -2 + 6 = 4
y = x + 6 = -0 + 6 = 6
y = x + 6 = 3 + 6 = 9
y = x + 6 = 5 + 6 = 11
y = x + 6 = 8 + 6 = 14

b.
y = 2x – 2

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
out put = input – 2
y = 2x – 2 = 2 x 0 – 2 = -2
y = 2x – 2 = 2 x 1 – 2 = 0
y = 2x – 2 = 2 x 3 – 2 = 4
y = 2x – 2 = 2 x 5 – 2 = 8
y = 2x – 2 = 2 x 8 – 2 = 14
y = 2x – 2 = 2 x 10 – 2 = 18

c.
y = x – 7

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
out put = input – 7
y = x – 7
y = x – 7 = 0 – 7 = -7
y = x – 7 = 5 – 7 = -2
y = x – 7 = 7 – 7 = 0
y = x – 7 = 10 – 7 = 3
y = x – 7 = 15 – 7 = 8

Question 2.
a.
y = x2 – 3

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y = x2 – 3 = -32 – 3 = 6
y = x2 – 3 = -22 – 3 = 1
y = x2 – 3 = -12 – 3 = -2
y = x2 – 3 = 02 – 3 = -3
y = x2 – 3 = 32 – 3 = 6

b.
y = $$\frac{x}{4}$$

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y = $$\frac{x}{4}$$ = Ā $$\frac{-8}{4}$$ = -2
y = $$\frac{x}{4}$$ = Ā $$\frac{-4}{4}$$ =-1
y = $$\frac{x}{4}$$ = Ā $$\frac{4}{4}$$ = 1
y = $$\frac{x}{4}$$ = Ā $$\frac{8}{4}$$ = 2
y = $$\frac{x}{4}$$ = Ā $$\frac{12}{4}$$ = 3

c.
y = $$\frac{x}{2}$$ – 1

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y = $$\frac{x}{2}$$ – 1 = $$\frac{-10}{2}$$ – 1 = -6
y = $$\frac{x}{2}$$ – 1 = $$\frac{-6}{2}$$ – 1 = -4
y = $$\frac{x}{2}$$ – 1 = $$\frac{-2}{2}$$ – 1 = -2
y = $$\frac{x}{2}$$ – 1 = $$\frac{2}{2}$$ – 1 = 0
y = $$\frac{x}{2}$$ – 1 = $$\frac{4}{2}$$ – 1 = 1

Question 3.
a.
y = 3x + 2

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y = 3x + 2 = 3 x -3 + 2 =-9+2 = -7
y = 3x + 2 = 3 x -2 + 2 =-6 + 2 = -4
y = 3x + 2 = 3 x 0 + 2 =0 + 2 = 2
y = 3x + 2 = 3 x 2 + 2 =6 + 2 = 8
y = 3x + 2 = 3 x 5 + 2 = 15 + 2 = 17

b.
y = (2 + x) Ć· 3

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y = (2 + x) Ć· 3 = (2 + -8) Ć· 3 = -2
y = (2 + x) Ć· 3 = (2 + -5) Ć· 3 = -1
y = (2 + x) Ć· 3 = (2 + 1) Ć· 3 = 1
y = (2 + x) Ć· 3 = (2 + 4) Ć· 3 = 2
y = (2 + x) Ć· 3 = (2 + 7) Ć· 3 = 3

c.
y = $$\frac{x}{3}$$ + 3

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y = $$\frac{x}{3}$$ + 3 = $$\frac{-9}{3}$$ + 3 = 0
y = $$\frac{x}{3}$$ + 3 = $$\frac{-6}{3}$$ + 3 = 1
y = $$\frac{x}{3}$$ + 3 = $$\frac{-3}{3}$$ + 3 = 2
y = $$\frac{x}{3}$$ + 3 = $$\frac{3}{3}$$ + 3 = 4
y = $$\frac{x}{3}$$ + 3 = $$\frac{6}{3}$$ + 3 = 5

Complete each function table for the given function.

Question 1.
a. y = 9x – 4

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y = 9x – 4 = 9x-10 – 4 = -94
y = 9x – 4 = 9x-6 – 4 = -58
y = 9x – 4 = 9x-2 – 4 = -22
y = 9x – 4 = 9×5 – 4 = 41
y = 9x – 4 = 9×12 – 4 = 104

b. y = $$\frac{x}{2}$$ + 2

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y = $$\frac{x}{2}$$ + 2 = $$\frac{-22}{2}$$ + 2 = -9
y = $$\frac{x}{2}$$ + 2 = $$\frac{-8}{2}$$ + 2 = -2
y = $$\frac{x}{2}$$ + 2 = $$\frac{2}{2}$$ + 2 = 3
y = $$\frac{x}{2}$$ + 2 = $$\frac{12}{2}$$ + 2 = 8
y = $$\frac{x}{2}$$ + 2 = $$\frac{22}{2}$$ + 2 = 13

c. y = x – 4

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y = x – 4 = -23 – 4 = -27
y = x – 4 = -11 – 4 = -15
y = x – 4 = -4 – 4 = -8
y = x – 4 = 11 – 4 = 7
y = x – 4 = 22 – 4 = 18

Question 2.
a. y = x + 3

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y = x + 3 = Ā -15 + 3 = -12
y = x + 3 =Ā  -9 + 3 = -6
y = x + 3 =Ā  2 + 3 = 5
y = x + 3 =Ā  8 + 3 = 11
y = x + 3 =Ā  14 + 3 = 17

b. y = 2x – 6

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y = 2x – 6 = 2x – 21 – 6 = -48
y = 2x – 6 = 2x – 16 – 6 = -38
y = 2x – 6 = 2x – 7 – 6 = -20
y = 2x – 6 = 2x 13 – 6 = 20
y = 2x – 6 = 2x 24 – 6 = 42

c. y = $$\frac{x}{10}$$ + 5

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y = $$\frac{x}{10}$$ + 5 = $$\frac{-120}{10}$$ + 5 = -7
y = $$\frac{x}{10}$$ + 5 = $$\frac{-80}{10}$$ + 5 = -3
y = $$\frac{x}{10}$$ + 5 = $$\frac{30}{10}$$ + 5 = 8
y = $$\frac{x}{10}$$ + 5 = $$\frac{90}{10}$$ + 5 = 14
y = $$\frac{x}{10}$$ + 5 = $$\frac{100}{10}$$ + 5 = 15

Question 3.
a. y = 7x + 5

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y = 7x + 5 = 7x -11 + 5 = -77 +5 = -72
y = 7x + 5 = 7x -8 + 5 = -56 + 5 = -51
y = 7x + 5 = 7x -5 + 5 = -35 + 5 = -30
y = 7x + 5 = 7x -2 + 5 = -14 + 5 = -9
y = 7x + 5 = 7x 1+ 5 = 7 + 5 = 12

b. y = x Ć· 13

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y = x Ć· 13 = -182 Ć· 13 = -14
y = x Ć· 13 = -91 Ć· 13 = -7
y = x Ć· 13 = -26 Ć· 13 = -2
y = x Ć· 13 = 104 Ć· 13 = 8
y = x Ć· 13 = 195 Ć· 13 = 15

c. y = 3x + 24

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y = 3x + 24 = 3x -29 + 24 =-63
y = 3x + 24 = 3x -16 + 24 =-24
y = 3x + 24 = 3x 11 + 24 =-57
y = 3x + 24 = 3x 19 + 24 =-81
y = 3x + 24 = 3x 26 + 24 =102

Read each function. Experiment with values of x. Look for whole number values of x that create a whole number value for y (positive or negative). Once you find 5 numbers for x, fill in the function table for x and for y. Put the values of x in numerical order.

Question 1.
a. y = $$\frac{x}{2}$$ – 7

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y = $$\frac{x}{2}$$ – 7 = $$\frac{2}{2}$$ – 7= -6
y = $$\frac{x}{2}$$ – 7 = $$\frac{4}{2}$$ – 7= -5
y = $$\frac{x}{2}$$ – 7 = $$\frac{6}{2}$$ – 7= -4
y = $$\frac{x}{2}$$ – 7 = $$\frac{8}{2}$$ – 7= -3
y = $$\frac{x}{2}$$ – 7 = $$\frac{10}{2}$$ – 7= -2

b. y = $$\frac{x}{3}$$ – 7

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y is out put for a value x is input.
y = $$\frac{x}{3}$$ – 7 = $$\frac{-6}{3}$$ – 7 = -9
y = $$\frac{x}{3}$$ – 7 = $$\frac{-3}{3}$$ – 7 = -8
y = $$\frac{x}{3}$$ – 7 = $$\frac{6}{3}$$ – 7 = -5
y = $$\frac{x}{3}$$ – 7 = $$\frac{9}{3}$$ – 7 = -4
y = $$\frac{x}{3}$$ – 7 = $$\frac{12}{3}$$ – 7 = -3

c. y = $$\frac{x+4}{5}$$

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y is out put for a value x is input.
y = $$\frac{x+4}{5}$$ = $$\frac{-9+4}{5}$$ = -1
y = $$\frac{x+4}{5}$$ = $$\frac{-4+4}{5}$$ = 0
y = $$\frac{x+4}{5}$$ = $$\frac{1+4}{5}$$ = 1
y = $$\frac{x+4}{5}$$ = $$\frac{6+4}{5}$$ = 2
y = $$\frac{x+4}{5}$$ = $$\frac{11+4}{5}$$ = 3

Question 2.
a. y = 9x – 3

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y is out put for a value x is input.
y = 9x – 3 = 9(-1) – 3 = -12
y = 9x – 3 = 9(0) – 3 = -3
y = 9x – 3 = 9(1) – 3 = 6
y = 9x – 3 = 9(2) – 3 = 15
y = 9x – 3 = 9(3) – 3 = 24

b. y = $$\frac{x^{2}}{2}$$

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y is out put for a value x is input.
y = $$\frac{x^{2}}{2}$$ = $$\frac{-2^{2}}{2}$$ = 2
y = $$\frac{x^{2}}{2}$$ = $$\frac{0^{2}}{2}$$Ā  = 0
y = $$\frac{x^{2}}{2}$$ = $$\frac{2^{2}}{2}$$ = 2
y = $$\frac{x^{2}}{2}$$ = $$\frac{4^{2}}{2}$$ = 8
y = $$\frac{x^{2}}{2}$$ = $$\frac{6^{2}}{2}$$ = 18

c. y = 2 – $$\frac{x}{6}$$

Explanation:
A function is a relationship between two variables which results in only one output value for each input value.
y is out put for a value x is input.
y = 2 – $$\frac{x}{6}$$ = 2 – $$\frac{-6}{6}$$ = 3
y = 2 – $$\frac{x}{6}$$ = 2 – $$\frac{0}{6}$$ = 2
y = 2 – $$\frac{x}{6}$$ = 2 – $$\frac{6}{6}$$ = 1
y = 2 – $$\frac{x}{6}$$ = 2 – $$\frac{12}{6}$$ = 0
y = 2 – $$\frac{x}{6}$$ = 2 – $$\frac{18}{6}$$ = -1

Read each function table. See if you can identify the function it represents.

Question 3.
a.

y = _____
y = x – 1

Explanation:
y is out put for a value and x is input.
With reference to the given function table,
y = x – 1
y = x – 1 = -2 -1 = -3
y = x – 1 = -1 – 1 = -2
y = x – 1 = 0 – 1 = -1
y = x – 1 = 1 – 1 = 0
y = x – 1 = 2 – 1 = 1

b.

y = _____
y = -3x

Explanation:
y is out put for a value x is input.
With reference to the given function table,
y = -3x
y = -3x = -3 (0) = 0
y = -3x = -3 (1) = -3
y = -3x = -3 (2) = -6
y = -3x = -3 (3) = -9
y = -3x = -3 (5) = -15

c.

y = ____
y = $$\frac{x}{2}$$ + 1

Explanation:
y is out put for a value x is input.
With reference to the given function table,
y = $$\frac{x}{2}$$ + 1
y = $$\frac{-4}{2}$$ + 1 = -2 + 1 = -1
y = $$\frac{-2}{2}$$ + 1 = -1 + 1 = 0
y = $$\frac{0}{2}$$ + 1 = 0 + 1 = 1
y = $$\frac{2}{2}$$ + 1 = 1 + 1 = 2
y = $$\frac{4}{2}$$ + 1 = 2 + 1 = 3

d.

y = ____
y = -5x – 6

Explanation:
y is out put for a value x is input.
With reference to the given function table,
y = -5x – 6
y = -5 (-3) – 6 = 15 – 6 =Ā  9
y = -5 (-2) – 6 = 10 – 6 = 4
y = -5 (0) – 6 = – 6
y = -5(1) – 6 = -5 – 6 = – 11
y = -5(2) – 6 = -10 -6 = -16

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