Question:
Draw the graphs described below and answer the question for each.
A. Draw the graph of a line with an undefined slope. Write the equation of the line you drew.
B. If you wrote the first letter of your LAST NAME (upper-case letter) on a coordinate plane, would it be a function? Make a sketch and provide an explanation as to how you determined whether it is a function or not.
Solution:
A.
Remember that any line that has an undefined slope is a vertical line, that has no y-intercept. Therefore the equation of a line with an undefined slope is x = a, where a = x-intercept.
we can conclude that the correct answer is:
According to this information, we can take the following equation for a line with an undefined slope:
and its graph would be:
B. Remember that a simple visual way to determine if a particular graph is a function is by imagining vertical lines passing through it. If the vertical line touches more than once, it is not a function.
For example, consider the curve that represents the letter O:
And notice that the above curve is a circle and note also the following fact:
We can conclude that the correct answer is:
The curve of the letter O is not a function, since a line intersects at two points of this line.