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

Question

xx minus, 3−3 minus, 2−2 minus, 1−1 00 11
f, of, xf(x) 17821782 29702970 49504950 82508250 1375013750
Answer
Attempt 1 out of 2

This function is
because
.

Answer 1

To determine the nature of the function depicted in the table, let's first look at the pairs given:

• $f(-3)=1782$
• $f(-2)=970$
• $f(-1)=4950$
• $f(0)=8250$
• $f(1)=13750$

Now, we need to analyze how the outputs change as the inputs change.

1. Identify the output values:
   • At $x=-3$, the output is 1782.
   • At $x=-2$, the output is 970. (Decreases)
   • At $x=-1$, the output is 4950. (Increases)
   • At $x=0$, the output is 8250. (Increases)
   • At $x=1$, the output is 13750. (Increases)

Given the changes in the outputs, we can observe that the function does not follow a linear or simple polynomial form because the decrease at $-2$ and the variable increases suggest a more complex relationship.

Next, let's consider the possibility of a quadratic or exponential function. To go further, we can look at the ratios or check for a common pattern in differences, but without those calculations presented, we'll focus on defining the function type based on its behavior.

Given the values:

• The function values have non-consistent intervals and appear to be changing rapidly, hinting towards a polynomial or exponential nature.

To summarize:

This function is not linear because the changes in output do not correspond to a constant change as seen in a linear function. The outputs rapidly increase especially around zero.

Answer
This function is non-linear because the rate of change of the function values is not constant, and the input-output relationship does not fit a straight line (it involves varying increments).