The considered step function is discontinuous at Option C: multiples of 8 greater than 0. A gift card in the amount of $25 will purchase _3_ movies.
What is a continuous function?
A function [tex]y = f(x)[/tex] is said to be continuous at x = [tex]x_0[/tex] if:
- Left sided limit of the function on x = [tex]x_0[/tex] exist and are finite.
- Right sided limit of the function on x = [tex]x_0[/tex] exist and are finite.
- Both sided limits are equal to the value of the function at x = [tex]x_0[/tex].
For this case, the step function is always discontinous on the points of its input where it steps up or down, and is continous elsewhere.
We see that the function is stepping up on multiples of 8.
Assuming the function is defined for values > 0, we deduce that the function is discontinous on multiples of 8 greater than 0.
At x = 25 (dollars) the value of the function is y = 3 (the number of movies), as visible in the graph.
Thus, the considered step function is discontinuous at Option C: multiples of 8 greater than 0. A gift card in the amount of $25 will purchase _3_ movies.
Learn more about discontinuous functions here:
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