Question

Function A: Function B: Function C: y=x+5

(4 points)
Which function has a negative rate of change (slope)?

Which function has the smallest y-intercept?

Which function would you want to represent your money earned per hour?

Which function would give you the highest initial amount of money?

1 answer

To answer your questions, we need to analyze the slopes and y-intercepts of the given functions:

Which function has a negative rate of change (slope)?
- The rate of change (slope) indicates how much \(y\) changes for a unit change in \(x\). A negative slope means that as \(x\) increases, \(y\) decreases. Since we only see Function A and the equation for Function C (\(y = x + 5\)), we don't have specific functions for A and B. However, if we assume Function A and Function B have negative slopes (e.g. functions like \(y = -x + c\)),
  - Choose Function A or B if they are indeed negative. If C were the only one, it has a positive slope (+1).
Which function has the smallest y-intercept?
- The y-intercept is the value of \(y\) when \(x = 0\). For Function C, the y-intercept is 5 (when \(x = 0\)). Without specific details about Functions A and B, we cannot definitively answer this without knowing their forms.
Which function would you want to represent your money earned per hour?
- Generally, a positive slope represents earnings (money earned increases with time). Therefore, if Function C is the only one considered and has a slope of +1, it would be the preferred choice since it indicates a positive income per hour.
Which function would give you the highest initial amount of money?
- The highest initial amount of money is represented by the function with the highest y-intercept. Again, if we only have Function C at a y-intercept of 5, we need the y-intercepts of Functions A and B to determine the highest.

If you provide specific forms of Functions A and B, I can give you accurate answers for all queries.