Question

Y=-1/2x^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 \( y = -\frac{1}{2}x^3 \), we need to calculate the corresponding \( y \) values for five different \( x \) values — one at \( x = 0 \), two negative, and two positive.

Let's calculate the points:

1. **For \( x = 0 \)**:
\[
y = -\frac{1}{2}(0)^3 = 0 \quad \Rightarrow \quad (0, 0)
\]

2. **For \( x = -1 \)**:
\[
y = -\frac{1}{2}(-1)^3 = -\frac{1}{2}(-1) = \frac{1}{2} \quad \Rightarrow \quad (-1, \frac{1}{2})
\]

3. **For \( x = -2 \)**:
\[
y = -\frac{1}{2}(-2)^3 = -\frac{1}{2}(-8) = 4 \quad \Rightarrow \quad (-2, 4)
\]

4. **For \( x = 1 \)**:
\[
y = -\frac{1}{2}(1)^3 = -\frac{1}{2}(1) = -\frac{1}{2} \quad \Rightarrow \quad (1, -\frac{1}{2})
\]

5. **For \( x = 2 \)**:
\[
y = -\frac{1}{2}(2)^3 = -\frac{1}{2}(8) = -4 \quad \Rightarrow \quad (2, -4)
\]

Now, we have the following five points:
1. \( (0, 0) \)
2. \( (-1, \frac{1}{2}) \)
3. \( (-2, 4) \)
4. \( (1, -\frac{1}{2}) \)
5. \( (2, -4) \)

To visualize the graph, you would plot these points on the coordinate system, and you'll see the nature of the cubic function \( y = -\frac{1}{2}x^3 \), which is decreasing for positive \( x \) and increasing for negative \( x \).

If you're using specific graphing software or an online graphing tool, you would input this function to see the overall graph and then add the calculated points. If you have a button for graphing the function, be sure to highlight or click it after inputting the function.