Question

graph y = 2 (5 - 3x3) - 6 + 9x11

Answer 1

graph form points

Answer 2

To graph the expression \( y = 2(5 - 3x^3) - 6 + 9x^{11} \), we will first simplify it:

1. Distribute the 2:
\[
y = 2 \cdot 5 - 2 \cdot 3x^3 - 6 + 9x^{11}
\]
\[
= 10 - 6 + 9x^{11} - 6x^3
\]

2. Combine the constant terms:
\[
y = 4 + 9x^{11} - 6x^3
\]

Now the equation is simplified to:
\[
y = 4 + 9x^{11} - 6x^3
\]

### Graphing the Function

To graph the function \( y = 4 + 9x^{11} - 6x^3 \), you can follow these steps or use software/graphing calculators:

1. **Determine key points**: Evaluate the function at various values of \( x \) (for example, -2, -1, 0, 1, 2) to find corresponding \( y \) values.
2. **Identify end behavior**: As \( x \) approaches large positive or negative values, the \( 9x^{11} \) term will dominate, leading to \( y \) heading towards positive infinity as \( x \) increases and also negative infinity as \( x \) decreases.
3. **Sketch the graph**: Plot the calculated points and sketch the curve. The function will be very steep for larger absolute values of \( x \) due to the \( x^{11} \) term.

### Summary of Behavior
- The graph will be a polynomial of degree 11.
- It will have a general shape that rises steeply for large (positive) \( x \) and drops heavily for large (negative) \( x \).
- The presence of the \( -6x^3 \) term will influence the shape and may create local minima/maxima, but for most \( x \), the \( 9x^{11} \) term will dominate.

Graphing can be done effectively using graphing software or a graphing calculator for more precise points and visualization.

Answer 3

To graph the function \( y = 4 + 9x^{11} - 6x^3 \) by determining specific points, we will evaluate the function at various values of \( x \). Here are some sample calculations:

### Points Calculation

Let's evaluate \( y \) at the following values of \( x \): -2, -1, 0, 1, 2.

1. **For \( x = -2 \)**:
\[
y = 4 + 9(-2)^{11} - 6(-2)^3
\]
\[
= 4 + 9(-2048) - 6(-8)
\]
\[
= 4 - 18432 + 48
\]
\[
= 4 - 18432 + 48 = -18380
\]
So, the point is \( (-2, -18380) \).

2. **For \( x = -1 \)**:
\[
y = 4 + 9(-1)^{11} - 6(-1)^3
\]
\[
= 4 + 9(-1) - 6(-1)
\]
\[
= 4 - 9 + 6
\]
\[
= 1
\]
So, the point is \( (-1, 1) \).

3. **For \( x = 0 \)**:
\[
y = 4 + 9(0)^{11} - 6(0)^3
\]
\[
= 4 + 0 - 0 = 4
\]
So, the point is \( (0, 4) \).

4. **For \( x = 1 \)**:
\[
y = 4 + 9(1)^{11} - 6(1)^3
\]
\[
= 4 + 9 - 6
\]
\[
= 7
\]
So, the point is \( (1, 7) \).

5. **For \( x = 2 \)**:
\[
y = 4 + 9(2)^{11} - 6(2)^3
\]
\[
= 4 + 9(2048) - 6(8)
\]
\[
= 4 + 18432 - 48
\]
\[
= 4 + 18432 - 48 = 18388
\]
So, the point is \( (2, 18388) \).

### Summary of Points

We have the following points:

- \( (-2, -18380) \)
- \( (-1, 1) \)
- \( (0, 4) \)
- \( (1, 7) \)
- \( (2, 18388) \)

### Graphing the Points

You can plot these points on a Cartesian coordinate system. Given the extreme values for \( y \) when \( x = -2 \) and \( x = 2 \), you will observe the rapid growth of the function due to the \( 9x^{11} \) term's influence, leading to a steep curve.

1. **Plot the points on a graph**.
2. **Connect them smoothly** to reflect the polynomial nature of the function.
3. **Consider the end behavior** where as \( x \) approaches \( \pm \infty \), \( y \) approaches \( \pm \infty \).

This will give you a visual understanding of how the function behaves. If you have graphing software or a graphing calculator, it can help visualize this polynomial more accurately.