Question

Use an input-output table to determine which graph accurately represents the function f(x)=20x+45
, using the given inputs.
Desmos calculator

Input Output
4
6
8
10


12


(1 point)
Responses








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Answer 1

To determine which graph accurately represents the function \( f(x) = 20x + 45 \) using an input-output table, we need to calculate the output values for the given inputs (4, 6, 8, 10, and 12).

Let's calculate the output for each input:

1. For \( x = 4 \):
\[
f(4) = 20(4) + 45 = 80 + 45 = 125
\]

2. For \( x = 6 \):
\[
f(6) = 20(6) + 45 = 120 + 45 = 165
\]

3. For \( x = 8 \):
\[
f(8) = 20(8) + 45 = 160 + 45 = 205
\]

4. For \( x = 10 \):
\[
f(10) = 20(10) + 45 = 200 + 45 = 245
\]

5. For \( x = 12 \):
\[
f(12) = 20(12) + 45 = 240 + 45 = 285
\]

Now we can summarize the input-output table:

| Input | Output |
|-------|--------|
| 4 | 125 |
| 6 | 165 |
| 8 | 205 |
| 10 | 245 |
| 12 | 285 |

With these output values, you can graph the points (4, 125), (6, 165), (8, 205), (10, 245), and (12, 285) on the Desmos calculator or any graphing tool.

Finally, check which graph correctly represents the line corresponding to these points. The graph should be a straight line with a positive slope, indicative of a linear function, specifically one that has a y-intercept of 45 and rises steeply due to the coefficient of \( x \) being 20.

Based on these calculated values, you can identify the correct graph that matches these points.