Use the table to answer the question.

Question

x	y
0	3
1	312
3
1
2
2	4
3	412
4
1
2
Which of the following equations describes the function in the table using function notation?

(1 point)
Responses

f(x)=3x+12
𝑓
(
𝑥
)
=
3
𝑥
+
1
2
f left parenthesis x right parenthesis equals 3 x plus Start Fraction 1 over 2 End Fraction

f(y)=3x+12
𝑓
(
𝑦
)
=
3
𝑥
+
1
2
f left parenthesis y right parenthesis equals 3 x plus Start Fraction 1 over 2 End Fraction

f(y)=12x+3
𝑓
(
𝑦
)
=
1
2
𝑥
+
3
f left parenthesis y right parenthesis equals Start Fraction 1 over 2 End Fraction x plus 3

f(x)=12x+3

GPT-4o mini · Answer

To determine the correct function notation for the data in the table, we need to analyze the provided data points. The table shows pairs of $x$ and $y$ values, but part of it seems to be missing. Let's assume the complete pairs are:

When $x = 0$ , $y = 3$
When $x = 1$ , $y = 312$
When $x = 2$ , $y = 4$
When $x = 3$ , $y = 412$
When $x = 4$ , $y = 1$

Note that there seem to be inconsistencies in expected behavior (for example, $y$ is much larger for some $x$ values). However, to find a function that might fit a pattern, we should examine it.

Looking through the answer choices:

$f (x) = 3 x + 12$
$f (x) = 3 x + \frac{1}{2}$
$f (y) = 3 x + 12$
$f (y) = 3 x + \frac{1}{2}$
$f (y) = 12 x + 3$
$f (y) = \frac{1}{2} x + 3$
$f (x) = 12 x + 3$

Unfortunately, the provided data does not lend itself clearly to a simple linear equation, nor does it clarify which pair of $x$ and $y$ you want to evaluate with more context.

However, let's look at the answers: Only equations $f (x)$ would likely be acceptable, as $f (y)$ suggests a different approach.

Assuming points dropped in are misaligned, let’s summarize likely relationships manually if:

If we found that at point (0,3), for instance, we might pick $f (x) = 3$ (a constant), but the growth of points leads to more attention.

Testing simple relationships on $f (x)$ :

If $f (x) = 12 x + 3$ , then:
- When $x = 0$ , $y = 3$ ✓
- When $x = 1$ , $y = 12 + 3 = 15$ ×
- In other cases, too, values may violate even more.

Ultimately, without correct patterns being followed, if based accurately only on above, $f (x) = 12 x + 3$ could fit simple starting points yielding best fitting value at the lowest inputs.

If you need a precise fit, please double-check provided pairs in full table for any entries as numerical discrepancies alter observed trendlines.