Answer the questions below to determine what kind of function is depicted in the table below.

Question

xx 11 22 33 44 55
f, of, xf(x) 88 1313 1818 2323 2828
Answer
Attempt 1 out of 2

This function is
because
.

Answer 1

To determine the type of function depicted in the table provided, we first analyze the given values:

The values of \( x \) are:

• \( 1, 2, 3, 4, 5 \)

The corresponding values of \( f(x) \) are:

• \( 88, 1313, 1818, 2323, 2828 \)

From the provided information, we notice that the values of \( f(x) \) appear to have a pattern. If we look closely:

1. When \( x = 1 \), \( f(1) = 88 \)
2. When \( x = 2 \), \( f(2) = 1313 \)
3. When \( x = 3 \), \( f(3) = 1818 \)
4. When \( x = 4 \), \( f(4) = 2323 \)
5. When \( x = 5 \), \( f(5) = 2828 \)

The output values seem to increase in jumps, giving a cue they may represent a quadratic behavior or a more complex polynomial. However, a more straightforward approach would include finding a specific formula or pattern.

By analyzing the output:

• For \( f(1) \) and \( f(2) \):

  • \( 1313 - 88 = 1225 \)

• For \( f(2) \) and \( f(3) \):

  • \( 1818 - 1313 = 505 \)

• For \( f(3) \) and \( f(4) \):

  • \( 2323 - 1818 = 505 \)

• For \( f(4) \) and \( f(5) \):

  • \( 2828 - 2323 = 505 \)

The differences aren't constant, so we can observe that the function appears to be quadratic because the rate of increase does not remain constant, and the first difference is not constant but the second difference (between increments) continues to be similar as we examine incremental growth.

In conclusion, we can say:

This function is quadratic because it appears that the second differences of the values of \( f(x) \) are constant, suggesting a parabolic relationship.