Question

Y=-13/8x^3
Plot five points on the graph of the function: one point with x=0, two points with negative x-values, and two points with positive x-values. Then click on the graph-a-function button.

Answer 1

To plot the function \( y = -\frac{13}{8}x^3 \), let's first find the corresponding \( y \)-values for the specified \( x \)-values:

### Points with Calculated \( y \)-Values:

1. **For \( x = 0 \)**:
\[
y = -\frac{13}{8}(0)^3 = 0 \implies (0, 0)
\]

2. **For \( x = -1 \)**:
\[
y = -\frac{13}{8}(-1)^3 = -\frac{13}{8}(-1) = \frac{13}{8} \implies (-1, \frac{13}{8}) \approx (-1, 1.625)
\]

3. **For \( x = -2 \)**:
\[
y = -\frac{13}{8}(-2)^3 = -\frac{13}{8}(-8) = \frac{104}{8} = 13 \implies (-2, 13)
\]

4. **For \( x = 1 \)**:
\[
y = -\frac{13}{8}(1)^3 = -\frac{13}{8} \implies (1, -\frac{13}{8}) \approx (1, -1.625)
\]

5. **For \( x = 2 \)**:
\[
y = -\frac{13}{8}(2)^3 = -\frac{13}{8}(8) = -13 \implies (2, -13)
\]

### Summary of Points:

- \( (0, 0) \)
- \( (-1, \frac{13}{8}) \) or approximately \( (-1, 1.625) \)
- \( (-2, 13) \)
- \( (1, -\frac{13}{8}) \) or approximately \( (1, -1.625) \)
- \( (2, -13) \)

### Visual Representation:

You can now plot these points on a coordinate system:

1. **(0, 0)**
2. **(-1, 1.625)**
3. **(-2, 13)**
4. **(1, -1.625)**
5. **(2, -13)**

After plotting these points, you can use the graphing tool to visualize the overall graph of the function \( y = -\frac{13}{8}x^3 \).

If you're using a graphing calculator or software, input the function and see how it creates the curve that connects these five points. The graph will show the characteristic "S" shape of a cubic function, where it decreases for positive \( x \) and increases for negative \( x \).