Question

The table represents the function . Fill in the blanks based on the information given in the table.

x f(x)
-4 -66
-3 -29
-2 -10
-1 -3
0 -2
1 -1
2 6


(3 points)
Is this a linear or nonlinear function? _____________

When , ___________

When , ___________

Answer 1

To determine whether the function represented by the table is linear or nonlinear, we can analyze the differences in the \( f(x) \) values as \( x \) increases.

1. **Calculate the differences:**

- For \( x = -4 \) to \( x = -3 \):
\[
f(-3) - f(-4) = -29 - (-66) = 37
\]
- For \( x = -3 \) to \( x = -2 \):
\[
f(-2) - f(-3) = -10 - (-29) = 19
\]
- For \( x = -2 \) to \( x = -1 \):
\[
f(-1) - f(-2) = -3 - (-10) = 7
\]
- For \( x = -1 \) to \( x = 0 \):
\[
f(0) - f(-1) = -2 - (-3) = 1
\]
- For \( x = 0 \) to \( x = 1 \):
\[
f(1) - f(0) = -1 - (-2) = 1
\]
- For \( x = 1 \) to \( x = 2 \):
\[
f(2) - f(1) = 6 - (-1) = 7
\]

The differences of \( f(x) \) are not consistent; they are \( 37, 19, 7, 1, 1, 7 \). Since the differences are not constant, the function is nonlinear.

2. **Fill in the blanks:**

- **Is this a linear or nonlinear function?** Nonlinear

3. **Complete the statements:**

- **When \( x = 0 \),** \( f(0) = -2 \)
- **When \( x = 2 \),** \( f(2) = 6 \)

So the answers are:

- **Is this a linear or nonlinear function?** Nonlinear
- **When \( x = 0 \),** \( f(0) = -2 \)
- **When \( x = 2 \),** \( f(2) = 6 \)