Which of the following describes the appearance of the graph at a zero whose multiplicity is one? Enter the number of the correct option.
Option #1: The graph crosses the x-axis.
Option #2: The graph touches the x-axis and turns around.
Option #3: There is not enough information provided.
Option #1: The graph crosses the x-axis.
Option #1: The graph crosses the x-axis.
To determine the appearance of the graph at a zero with multiplicity one, we first need to understand what a zero with multiplicity one means. In algebra, a zero (or root) of a function is a value of the independent variable (usually denoted as x) that makes the function equal to zero.
The multiplicity of a zero refers to how many times the factor corresponding to that zero appears in the equation. In this case, a zero with multiplicity one indicates that the corresponding factor appears once in the equation.
Now, let's look at the options:
Option #1: The graph crosses the x-axis.
When the graph crosses the x-axis at a zero, it means that the function changes sign as it passes through that point. This scenario typically occurs when the multiplicity of the zero is an odd number (1, 3, 5, etc.).
Option #2: The graph touches the x-axis and turns around.
When the graph touches the x-axis at a zero and turns around, it means that the function remains the same sign on both sides of that point. This situation usually occurs when the multiplicity of the zero is an even number (2, 4, 6, etc.).
Option #3: There is not enough information provided.
If the information given in the question does not specify the multiplicity of the zero, then it is not possible to determine the exact appearance of the graph at that zero just based on the given options.
Based on the information provided, Option #1 is the most appropriate choice as it describes the appearance of the graph when a zero with multiplicity one is present.