On a coordinate plane, 5 points are plotted. The points are (1, 3), (2, 6), (3, 12), (4, 24), (5, 48).
Given that,
[tex]\rm f(x) = 3\times 2^{x-1}[/tex]
We have to determine,
Which graph is the sequence defined by the function?
According to the question,
[tex]\rm f(x) = 3\times 2^{x-1}[/tex]
To determine the graph is the sequence defined by the function following all the steps given below.
On a coordinate plane, 6 points are plotted.
1. Substitute the point x = 0 in the function,
[tex]\rm f(x) = 3 \times 2^{x-1}\\\\f(x) = 3 \times 2^{(0-1)}\\\\f(x) = 3 \times 2^{-1}\\\\f(x) = 3 \times \dfrac{1}{2}\\\\ f(x) = \dfrac{3}{2}[/tex]
2. Substitute the point x = 1 in the function,
[tex]\rm f(x) = 3 \times 2^{x-1}\\\\f(x) = 3 \times 2^{(1-1)}\\\\f(x) = 3 \times 2^{0}\\\\f(x) = 3 \times 1\\\\ f(x) = 3[/tex]
3. Substitute the point x = 2 in the function,
[tex]\rm f(x) = 3 \times 2^{x-1}\\\\f(x) = 3 \times 2^{(2-1)}\\\\f(x) = 3 \times 2^{2}\\\\f(x) = 3 \times 2\\\\ f(x) = 6[/tex]
4. Substitute the point x = 3 in the function,
[tex]\rm f(x) = 3 \times 2^{x-1}\\\\f(x) = 3 \times 2^{(3-1)}\\\\f(x) = 3 \times 2^{2}\\\\f(x) = 3 \times 4\\\\ f(x) = 12[/tex]
5. Substitute the point x = 4 in the function,
[tex]\rm f(x) = 3 \times 2^{x-1}\\\\f(x) = 3 \times 2^{(4-1)}\\\\f(x) = 3 \times 2^{3}\\\\f(x) = 3 \times 8\\\\ f(x) = 24[/tex]
6. Substitute the point x = 5 in the function,
[tex]\rm f(x) = 3 \times 2^{x-1}\\\\f(x) = 3 \times 2^{(5-1)}\\\\f(x) = 3 \times 2^{4}\\\\f(x) = 3 \times 16\\\\ f(x) = 48[/tex]
Hence, On a coordinate plane, 5 points are plotted. The points are (1, 3), (2, 6), (3, 12), (4, 24), (5, 48).
For more details refer to the link given below.
https://brainly.com/question/18437368
