I am not asking directly for the answer to this problem, I just need help understanding how to work it.
Which of the following rules could be used to describe the function on the table below?
X | Y
-1|-1
0 | 1
1 | 3
a) f(x) = 2x
b) f(x) = 2x - 1
c) f(x) = 2x + 1
f(x) is the same thing as y so if you put y = 2x, and x = -1 that would make y = ?
x 3 4 5 6 7 8 9
y 6 8 9 12 14 16 18
To determine which rule describes the function in the table, we need to find the pattern between the input values (x) and the corresponding output values (y). Let's examine the differences between the input and output values:
- When x increases by 1 from -1 to 0, y increases by 2 from -1 to 1.
- When x increases by 1 from 0 to 1, y increases by 2 from 1 to 3.
Based on this pattern, we can observe that as x increases by 1, y increases by a constant value of 2.
Now, let's analyze the given options:
a) f(x) = 2x
If we plug in x=-1, we get f(-1) = 2(-1) = -2, which doesn't match the value of -1 in the table.
b) f(x) = 2x - 1
If we plug in x=-1, we get f(-1) = 2(-1) - 1 = -3, which doesn't match the value of -1 in the table.
c) f(x) = 2x + 1
If we plug in x=-1, we get f(-1) = 2(-1) + 1 = -1, which matches the value of -1 in the table. Furthermore, when we plug in x=0 and x=1, we get f(0) = 1 and f(1) = 3, which also match the corresponding values in the table.
Therefore, option c) f(x) = 2x + 1 accurately describes the function in the given table.