This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output. 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form  and the question asks to calculate  we know that the input value is six.

Step 2: Given the function, input the desired  value. 

In step one the input value of six was found. Now substitute 6 in for every in the function.

Step 3: Verify solution by graphing the function.

To find the function value on a graph go to  and find the y value that lies on the graph at . Looking at the graph above when , .

Recall that , thus verifying the solution found in step 2.

To solve this problem, first recall the equation of a line.

where

Remember that slope is the rate of change that occurs in a function and that the -intercept is the  value corresponding to an  value equalling zero.

Now, identify what is known.

"Billy buys a tomato plant that is 4 inches tall. With regular watering the plant grows 3 inches a year."

Since the height of Billy's plant is 4 inches tall when he gets it, at time being zero. It is also stated that the plant grows 3 inches per year, this is the rate of change of the plant's height. Writing the known information in mathematical terms results as follows.

In this case our 

Therefore, the -intercept represents the starting height of the plant which is 4 inches.

To solve this problem, first recall the equation of a line.

where

Remember that slope is the rate of change that occurs in a function and that the -intercept is the  value corresponding to an  value equalling zero.

Now, identify what is known.

"Billy buys a tomato plant that is 4 inches tall. With regular watering the plant grows 3 inches a year."

Since the height of Billy's plant is 4 inches tall when he gets it, at time being zero. It is also stated that the plant grows 3 inches per year, this is the rate of change of the plant's height. Writing the known information in mathematical terms results as follows.

In this case our 

Therefore, the slope represents the rate of change in the height of the plant which is 3 inches per year.

First calculate the slope of the line using the slope formula.

Substituting in the known information.

Now use point slope form to find the equation of the line passing through these points.

Now identify which point lies on the line.

Therefore, the point that lies on the line is (9,10)

To solve this problem first manipulate the given equation to solve for .

Multiply by  on both sides. The 's on the left hand side of the equation will cancel out.

Now to calculate , substitute the value for  that was just found, into the denominator and simplify by canceling out common factors.

First we group terms

Now we want to have a perfect square, so we add , and we subtract , so now it looks like

Simplify to get

We can use point slope form to determine the equation of a line that fits the data. 

Point slope form is , where , and  is the slope, where .

Let , , , and .

If we do this for every other point, we will see that they have the same slope of .

Now let , and .

If we use the equation that solved for previously, , we just plug in  for .

The answer is, "The estimated increase in the average number of college graduates each year" because the equation is a model, which is an estimation.