Question

Graph the function represented by the table below. Is the function linear or​ nonlinear?
x
0
1
2
3
4
y
0
1
negative 5
8
negative 8
Question content area bottom left
Part 1
Graph the function.
Is the function linear or​ nonlinear? Choose the correct answer below.
The function is linear.
The function is nonlinear.

Answer 1

To determine whether the function represented by the table is linear or nonlinear, we can analyze the values of \( y \) for the corresponding \( x \) values.

**Given values:**
\[
\begin{align*}
x & : 0, 1, 2, 3, 4 \\
y & : 0, 1, -5, 8, -8
\end{align*}
\]

### Step 1: Graph the points

Let's plot the points:

- \( (0, 0) \)
- \( (1, 1) \)
- \( (2, -5) \)
- \( (3, 8) \)
- \( (4, -8) \)

### Step 2: Check for a consistent slope

For a function to be linear, the difference in \( y \) values divided by the difference in \( x \) values (the slope) must be constant.

1. From \( (0, 0) \) to \( (1, 1) \):
- Slope = \( \frac{1 - 0}{1 - 0} = \frac{1}{1} = 1 \)

2. From \( (1, 1) \) to \( (2, -5) \):
- Slope = \( \frac{-5 - 1}{2 - 1} = \frac{-6}{1} = -6 \)

3. From \( (2, -5) \) to \( (3, 8) \):
- Slope = \( \frac{8 - (-5)}{3 - 2} = \frac{13}{1} = 13 \)

4. From \( (3, 8) \) to \( (4, -8) \):
- Slope = \( \frac{-8 - 8}{4 - 3} = \frac{-16}{1} = -16 \)

### Step 3: Conclusion

Since the slopes between different points are not constant (1, -6, 13, -16), the function does not represent a straight line and is therefore **nonlinear**.

### Answer:
**The function is nonlinear.**