15. Rhianna is trying to determine how quickly a salmon can swim with the current versus against the current. She is using a polynomial equation to make her calculations. When she graphs the equation
what will the shape be?
0
a repeating wave
о
a line that bounces back and forth over the x-axis
о
a J-shaped line
a horizontally stretched S-shaped line



Answer :

To determine the shape of the graph that Rhianna will obtain from a polynomial equation, let's analyze the options:

1. A repeating wave:
- Repeating wave patterns are typically associated with trigonometric functions like sine and cosine. These functions have regular oscillations and are not characteristic of polynomial equations.

2. A line that bounces back and forth over the x-axis:
- Polynomial equations can indeed create graphs that cross the x-axis multiple times. The degree of the polynomial determines the number of possible turning points (where the graph changes direction), and these often result in a graph that may seem to "bounce" back and forth over the x-axis.

3. A J-shaped line:
- This shape is usually indicative of exponential functions, which have rapid growth or decay. Polynomial equations generally do not exhibit this simple, curved shape.

4. A horizontally stretched S-shaped line:
- This is characteristic of a cubic polynomial function (degree 3) or higher-order polynomials that have similar shapes. While this is possible for polynomials, it does not capture the general tendency for higher-degree polynomials that can cross the x-axis multiple times.

Given the choices, the option that best fits the behavior of polynomial equations, which can exhibit multiple crossings at the x-axis and changing directions, is:

A line that bounces back and forth over the x-axis

Thus, the graph of Rhianna's polynomial equation will have the shape of a line that bounces back and forth over the x-axis.