ITEM 3 - from the lesson Function Representations.
Select the correct input-output table to represent the function below.
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(
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)
=
−
4
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+
5
f(x)=−4x+5
Input (x) Output (f(x))
-------------------------------
1 1
2 -3
3 -7
4 -11
5 -15
To represent the function f(x) = -4x + 5 in an input-output table, we need to determine the outputs for different inputs and list them in the table.
Let's choose a few values for x and calculate the corresponding values for f(x):
When x = 0:
f(0) = -4(0) + 5 = 0 + 5 = 5
When x = 1:
f(1) = -4(1) + 5 = -4 + 5 = 1
When x = 2:
f(2) = -4(2) + 5 = -8 + 5 = -3
When x = -1:
f(-1) = -4(-1) + 5 = 4 + 5 = 9
Now, we can fill in the input-output table:
x | f(x)
---------
0 | 5
1 | 1
2 | -3
-1 | 9
Therefore, the correct input-output table to represent the function f(x) = -4x + 5 is:
x | f(x)
---------
0 | 5
1 | 1
2 | -3
-1 | 9
To select the correct input-output table to represent the function f(x) = -4x + 5, we need to understand how the function works.
The function f(x) = -4x + 5 represents a linear equation, where the coefficient of x is -4 and the constant term is 5. This means that for any given input value of x, the function will calculate the output by multiplying x by -4, and then adding 5 to the result.
To create an input-output table, we need to choose values for x and calculate the corresponding values of f(x). Let's consider a few values of x and calculate f(x) for each one:
x = 0:
f(0) = -4(0) + 5
f(0) = 0 + 5
f(0) = 5
x = 1:
f(1) = -4(1) + 5
f(1) = -4 + 5
f(1) = 1
x = -1:
f(-1) = -4(-1) + 5
f(-1) = 4 + 5
f(-1) = 9
x = 2:
f(2) = -4(2) + 5
f(2) = -8 + 5
f(2) = -3
To construct the input-output table, we list the x-values in one column and the corresponding f(x) values in another column:
x | f(x)
-----------
0 | 5
1 | 1
-1 | 9
2 | -3
Based on the calculations above, the correct input-output table to represent the function f(x) = -4x + 5 is:
x | f(x)
-----------
0 | 5
1 | 1
-1 | 9
2 | -3