Answer:
A)
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, ..