Write a rule for the linear function in the table.
x
f(x)
–4
16
0
0
4
–16
8
–32
A. f(x) = –4x
B. f(x) = x + 16
C. f(x) = 4x
D. f(x) = x
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-4(?) = 16
0(?)= 0
4(?) = -16
8(?) = -32
x(?) = ????
mmmh, sure looks like f(x) = -4x
write a rule for the linear function in the table x 1, 2,3,4, f(x) -7, -10,-13,-16
Write a rule for the linear function in the table.
x
f(x)
1
3
2
2
3
1
4
0
To identify the rule for the linear function, we need to determine the relationship between the input variable (x) and the output variable (f(x)) based on the information provided in the table.
One approach is to look for a consistent pattern in the changes between the x-values and the corresponding f(x)-values. From the given table, we observe that the relationship between x and f(x) is linear as the change in f(x) is proportional to the change in x.
Let's find the difference between the x-values and the f(x)-values:
x: -4, 0, 4, 8
f(x): 16, 0, -16, -32
The difference between consecutive x-values is always 4 (0 - (-4) = 4 - 0 = 4). Additionally, the difference between consecutive f(x)-values is also constant (-32 - (-16) = -16 - 0 = -16).
The constant rate of change indicates that the linear function has a slope of -16/4 = -4/1 = -4.
Next, we need to determine the y-intercept, which is the value of f(x) when x is 0. In the given table, when x = 0, f(x) is also 0.
Therefore, the rule for the linear function based on the table is f(x) = -4x + 0. Simplifying the equation, we get f(x) = -4x.
Comparing the rule with the given options, we find that option A matches our determined rule:
A. f(x) = –4x
So, the correct answer is A.