Which of the following describes the appearance of the graph at a zero whose multiplicity is one? Enter the number of the correct option.
1) The graph intersects the x-axis at a nonzero point.
2) The graph is tangent to the x-axis.
3) The graph is flat at the x-axis.
4) The graph has a sharp corner at the x-axis.
5) None of the above.
To accurately answer your question, please provide the options you are referring to.
To determine the appearance of the graph at a zero whose multiplicity is one, we need to understand the concept of multiplicity in relation to zeros of a function.
In mathematics, when we say that a number is a zero of a function, it means that plugging in that number into the function will result in an output of zero. The multiplicity of a zero refers to the number of times that zero appears as a factor in the function.
Now, let's consider the options and their meanings:
Option a) The graph touches and changes sign. This describes the appearance of a zero with an odd multiplicity. When a zero has an odd multiplicity, the graph of the function will touch the x-axis at that point and change sign as it passes through the zero.
Option b) The graph passes through smoothly. This describes the appearance of a zero whose multiplicity is one. When a zero has a multiplicity of one, the graph of the function will pass through the x-axis smoothly, without touching or changing sign at that point.
Option c) The graph bounces off the x-axis. This describes the appearance of a zero with an even multiplicity. When a zero has an even multiplicity, the graph of the function will bounce off the x-axis at that point.
Based on these explanations, the correct option for the appearance of the graph at a zero whose multiplicity is one would be option b) The graph passes through smoothly.