Use input-output tables to determine which graph accurately represents the function f(x)=12x+3 with inputs of −4, −2, 0, 2, and 4

Answer 1

First, we need to find the outputs for each input using the function f(x) = 12x + 3:

f(-4) = 12(-4) + 3 = -48 + 3 = -45
f(-2) = 12(-2) + 3 = -24 + 3 = -21
f(0) = 12(0) + 3 = 0 + 3 = 3
f(2) = 12(2) + 3 = 24 + 3 = 27
f(4) = 12(4) + 3 = 48 + 3 = 51

Now we can create an input-output table:

| x | f(x) |
|------|------|
| -4 | -45 |
| -2 | -21 |
| 0 | 3 |
| 2 | 27 |
| 4 | 51 |

Based on the values in the table, we can determine which graph represents the function f(x) = 12x + 3.

The graph that accurately represents the function f(x) = 12x + 3 will show a continuous line connecting the points (-4, -45), (-2, -21), (0, 3), (2, 27), and (4, 51). The line will have a positive slope of 12 and will pass through (0, 3).

Therefore, the graph that accurately represents the function f(x) = 12x + 3 is a line with a positive slope passing through the points (-4, -45), (-2, -21), (0, 3), (2, 27), and (4, 51).