Question

Use the table to answer the 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)=12x+3
f
(
x
)
=
1
2
x
+
3
f left parenthesis x right parenthesis equals Start Fraction 1 over 2 End Fraction x plus 3

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(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(x)=3x+12

Answer 1

whats the answer

Answer 2

To properly answer your question, I need to clarify that the table you provided is incomplete, and the values for \( x \) and \( y \) for some entries are missing. However, based on the provided pairs (0, 3), (1, 312), (2, 4), and (3, 412), I can help you analyze potential relationships.

1. The first pair (0, 3) suggests that when \( x = 0 \), \( y = 3 \).
2. The second pair (1, 312) suggests that when \( x = 1 \), \( y \) is much larger than the previous value.
3. The third entry you mention for \( x = 2 \) shows \( y = 4 \).
4. The fourth entry for \( x = 3 \) shows \( y = 412 \).

To identify which equation could describe this function, we can focus on the provided multiple choice options.

None of the equations presented appear to fit the pairs you listed completely, as they do not correspond well to linear progression or simply fit into the presented function forms without some of the missing values.

However, if we consider linear equations, we can rule out most of the given options, particularly considering the presence of rapid increases in \( y \) (like from 312 to 412).

Here is what we could conclude:

- \( f(x)=\frac{1}{2}x + 3 \) isn't likely because it couldn't correspond to the fast-growing \( y \) values seen.
- \( f(y)=\frac{1}{2}x + 3 \) is irrelevant as \( y \) should depend on \( x \), not the other way around.
- \( f(y)=3x + \frac{1}{2} \) is misleadingly structured, as it implies \( y \) is fed by varying \( x \) without a clear relationship.

Up to this point, the selection that seems most plausible based on common linear function decay is \( f(x) = 3x + 12 \), but the increasing nature of \( y \) values suggests that there might be a different polynomial or non-linear relationship.

Consider double-checking any missing data entries, as having those will be crucial in correctly identifying the best answer.

Answer 3

Based on the information provided, I cannot definitively determine the answer without knowing the complete and accurate pairs of \( (x, y) \). However, from the options provided, the equation that seems to align most closely with what a function could potentially look like is:

**f(x) = 3x + 12**

However, it’s important to note that this equation does not necessarily correspond to the pairs you provided, particularly because there seems to be a significant jump in values. Given that the values seem unusual, the dataset might require further validation.

If possible, double-check the table and ensure all \( (x, y) \) pairs are accurate before concluding. If the goal is strictly to choose from the presented options without extra validation, **f(x) = 3x + 12** would be the selected response. If providing a more accurate function based on all known values is possible, additional context might lead to a different best-fitting equation.