Question

Determine if the function below is linear or exponential then fill in the guided sentences below.
xx 22 33 44 55
f, of, xf(x) 44 minus, 4−4 minus, 12−12 minus, 20−20
Answer
Attempt 1 out of 2

The function is
because as xx increases, the yy values change
. The
of this function is exactly
.

Answer 1

this is wrong

Answer 2

To determine if the function is linear or exponential, we need to look at the relationship between the x values and their corresponding f(x) values provided in your data.

The data points are:
- When x = 2, f(x) = 44
- When x = 3, f(x) = 4
- When x = 4, f(x) = 12
- When x = 5, f(x) = 20

To identify if the function is linear or exponential, we can calculate the differences between f(x) values for consecutive x values:

- f(3) - f(2) = 4 - 44 = -40
- f(4) - f(3) = 12 - 4 = 8
- f(5) - f(4) = 20 - 12 = 8

The changes in f(x) are not constant; they vary as x increases. Therefore, we can see that it is not linear.

Now let's check if it is exponential by examining the ratios of the consecutive f(x) values:
- f(3) / f(2) = 4 / 44 = 1/11 ≈ 0.0909
- f(4) / f(3) = 12 / 4 = 3
- f(5) / f(4) = 20 / 12 = 5/3 ≈ 1.6667

Since the ratios of the f(x) values are not constant either, the function is not exponential, either.

Based on the examination, the function is nonlinear as neither type matches the data.

Here's how you can fill in the guided sentences:

1. The function is ***nonlinear*** because as xx increases, the yy values change ***in a way that does not exhibit a constant difference or ratio.***
2. The ***nature*** of this function is exactly ***neither linear nor exponential.***

Answer 3

I apologize for the confusion. Let's analyze the provided data points more carefully.

Your data appears to be:

| x | f(x) |
|----|------|
| 2 | 44 |
| 3 | 4 |
| 4 | 12 |
| 5 | 20 |

Now let's reevaluate the differences and examine the pattern:

1. **Values of f(x)**:
- At x = 2, f(2) = 44
- At x = 3, f(3) = 4
- At x = 4, f(4) = 12
- At x = 5, f(5) = 20

Now, let's find the differences:

- From x = 2 to x = 3: f(3) - f(2) = 4 - 44 = -40
- From x = 3 to x = 4: f(4) - f(3) = 12 - 4 = 8
- From x = 4 to x = 5: f(5) - f(4) = 20 - 12 = 8

The differences between f(x) values are not constant.

Next, let's check if the ratios of f(x) values for consecutive x values are constant:

- From x = 2 to x = 3: f(3) / f(2) = 4 / 44 = 1/11 (approximately 0.0909)
- From x = 3 to x = 4: f(4) / f(3) = 12 / 4 = 3
- From x = 4 to x = 5: f(5) / f(4) = 20 / 12 = 5/3 (approximately 1.6667)

The ratios between consecutive f(x) values are also not constant.

So, it is clear that this function does not present a linear or an exponential relationship.

Based on this information, the correct statement would be:

- The function is ***nonlinear*** because as x increases, the y values change ***in a non-constant manner.***
- The ***nature*** of this function is exactly ***neither linear nor exponential.***

If there’s anything specific you would like me to address or clarify, please let me know!