Select all points that must be on the graph of \(f\) if we know that \(f(2)=\text-4\) and \(f(5)=3.4\).

Write three statements that are true about this situation. Use function notation.

Function \(f\) gives the distance of a dog from a post, in feet, as a function of time, \(t\), in seconds, since its owner left.

Use the symbol \(=\) in at least one statement and the symbol \(<\) in another statement.

Elena writes the equation \(6x + 2y = 12\). Write a new equation that has:

1. exactly one solution in common with Elena’s equation
2. no solutions in common with Elena’s equation
3. infinitely many solutions in common with Elena’s equation

A restaurant owner wants to see if there is a relationship between the amount of sugar in some food items on her menu and how popular the items are. 

She creates a scatter plot to show the relationship between amount of sugar in menu items and the number of orders for those items. The correlation coefficient for the line of best fit is 0.58.

1. Are the two variables correlated? Explain your reasoning.
2. Does either of the variables cause the other to change? Explain your reasoning.