Which function describes the arithmetic sequence shown? −1, 1, 3, 5, 7, 9, 11, 13, a) ƒ(x) = 2x − 3 eliminate b) ƒ(x) = 3x − 2 c) ƒ(x) = 2x + 3 d) ƒ(x) = 3x + 2

A)

Step-by-step explanation:

Given:

The arithmetic sequence shown is −1, 1, 3, 5, 7, 9, 11, 13, ...

We have been given 4 options.

A) ƒ(x) = 2x − 3

B) ƒ(x) = 3x − 2

C) ƒ(x) = 2x + 3

D) ƒ(x) = 3x + 2

we will check for all and then find the correct 1

1) we will check for A) ƒ(x) = 2x − 3

When x=1; f(1) = 2×1 - 3 = -1

when x= 2; f(2) = 2×2 - 3 = 1

when x=3; f(3) = 2×3 - 3 = 3

when x=4; f(4) = 2×4 - 3 = 5

Hence the first four terms are similar to the given sequence hence we can conclude that this option is correct.

2) we will check for A) ƒ(x) = 3x − 2

When x=1; f(1) = 3×1 - 2 = 1

when x= 2; f(2) = 3×2 - 2 = 4

when x=3; f(3) = 3×3 - 2 = 7

when x=4; f(4) = 3×4 - 3 = 9

Hence the first four terms are not similar to the given sequence hence we can conclude that this option is incorrect.

3) we will check for A) ƒ(x) = 2x + 3

When x=1; f(1) = 2×1 + 3 = 5

when x= 2; f(2) = 2×2 + 3 = 7

when x=3; f(3) = 2×3 + 3 = 9

when x=4; f(4) = 2×4 + 3 = 11

Hence the first four terms are not similar to the given sequence hence we can conclude that this option is incorrect.

4) we will check for A) ƒ(x) = 3x + 2

When x=1; f(1) = 3×1 + 2 = 5

when x= 2; f(2) = 3×2 + 2 = 8

when x=3; f(3) = 3×3 + 2 = 11

when x=4; f(4) = 3×4 + 3 = 15

Hence the first four terms are not similar to the given sequence hence we can conclude that this option is incorrect.

Hence option A) ƒ(x) = 2x − 3 is the correct function which describes the the arithmetic sequence −1, 1, 3, 5, 7, 9, 11, 13, ..

where is the diagram? shown below where? ?

step-by-step explanation: