5. Which of the following are functions? The last two problems, i.e., b & c, are multi part relations consider all parts when determining whether or not these relations are functions. Explain your reasoning for a, b, and c.

a. f(x) = x + 3

b. f(x) = 73 if x>2 otherwise f(x) = -1

c. f(x) = 79if x>0 or f(x) = -9 if x<0 or f(x) = 9 or -9 if x = 0

c has two values of f(x) at x=0. Not allowed.

To determine whether these relations are functions, we need to check if each input (x) has a unique output (f(x)). Here's the analysis for each relation:

a. f(x) = x + 3:
This relation is a function. For any given x value, there is only one value for f(x) obtained by adding 3 to x. Each input has a unique output, so it satisfies the definition of a function.

b. f(x) = 73 if x > 2, otherwise f(x) = -1:
This relation is also a function. If x is greater than 2, the output is fixed at 73. If x is less than or equal to 2, the output is -1. Since there is a specific output for each input, it meets the criteria of a function.

c. f(x) = 79 if x > 0, or f(x) = -9 if x < 0, or f(x) = 9 or -9 if x = 0:
This relation is still a function. When x is greater than 0, the output is 79. When x is less than 0, the output is -9. When x is exactly 0, the output can be either 9 or -9. Although there are multiple outputs for x = 0, it still satisfies the definition of a function since all other inputs have unique outputs.

In summary, all three relations (a, b, and c) are functions.