Students can use the **Spectrum Math Grade 8 Answer Key** **Chapter 4 Lesson 4.2 Input/Output Tables**Ā 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

Answer:

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

Answer:

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

Answer:

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 = x^{2} – 3

Answer:

Explanation:

A function is a relationship between two variables which results in only one output value for each input value.

y = x^{2} – 3 = -3^{2} – 3 = 6

y = x^{2} – 3 = -2^{2} – 3 = 1

y = x^{2} – 3 = -1^{2} – 3 = -2

y = x^{2} – 3 = 0^{2} – 3 = -3

y = x^{2} – 3 = 3^{2} – 3 = 6

b.

y = \(\frac{x}{4}\)

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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 = \(\frac{x+4}{5}\)

Answer:

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

Answer:

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 = \(\frac{x^{2}}{2}\)

Answer:

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 – \(\frac{x}{6}\)

Answer:

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 = _____

Answer:

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 = _____

Answer:

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 = ____

Answer:

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 = ____

Answer:

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