Can someone help me with this question please?
A linear function may have zero, one, or infinitely many zeros. Illustarte all three of these situations.
Thank you!
Of course! I'm here to help.
To illustrate these three situations, we first need to understand what a linear function is. A linear function is a function where the highest degree of the variable is 1, and the graph of a linear function is always a straight line.
Now let's look at each situation:
1. Zero zeros: In this case, the linear function does not intersect the x-axis. This means that there are no values of x for which the function equals zero. The graph of a linear function with zero zeros would be a straight line that is either entirely above or below the x-axis, without crossing it.
2. One zero: In this case, the linear function intersects the x-axis at a single point (x-value) where the function equals zero. The graph of a linear function with one zero would be a straight line that passes through the x-axis at a specific point.
3. Infinitely many zeros: In this case, the linear function coincides with the x-axis for the entire range of x-values. In other words, every value of x makes the function equal to zero. The graph of a linear function with infinitely many zeros would be a straight line that lies entirely on the x-axis.
To better understand these situations, it might be helpful to plot some examples of linear functions on a graphing software or on paper.