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

Question

xx minus, 1−1 00 11 22 33
f, of, xf(x) 1010 1414 2626 4646 7474
Answer
Attempt 1 out of 2

This function is
because

Answer 1

To determine what kind of function is depicted in the provided table, let's analyze the values:

• When \( x = -1 \), \( f(x) = 10 \)
• When \( x = 0 \), \( f(x) = 14 \)
• When \( x = 1 \), \( f(x) = 26 \)
• When \( x = 2 \), \( f(x) = 46 \)
• When \( x = 3 \), \( f(x) = 74 \)

Next, let's look at the changes in \( f(x) \):

• From \( x = -1 \) to \( x = 0 \): \( 14 - 10 = 4 \)
• From \( x = 0 \) to \( x = 1 \): \( 26 - 14 = 12 \)
• From \( x = 1 \) to \( x = 2 \): \( 46 - 26 = 20 \)
• From \( x = 2 \) to \( x = 3 \): \( 74 - 46 = 28 \)

Now, let's analyze the differences of the differences:

• From \( 4 \) to \( 12 \): \( 12 - 4 = 8 \)
• From \( 12 \) to \( 20 \): \( 20 - 12 = 8 \)
• From \( 20 \) to \( 28 \): \( 28 - 20 = 8 \)

Since the second differences are constant (equal to 8), this indicates that the function is quadratic.

Therefore, we can conclude:

This function is quadratic because the second differences are constant.