Substitute 6x for x in the f(x) function and simplify.

Since we are given the functions x-intercepts, we can write the equation as , now we need to use FOIL.

Start with .

Now we do

What this question is asking for is to approximate the slope of the line of best fit. To calculate the slope, we need to find find two points on the line. The best points to pick out is , and . Now we can find the rate of change by using the following equation.

, where  are points on the line.

Break up the problem into parts.

Two times a number:  

 The sum of two times a number and forty:  

Is equal to sixteen:  

Combine the terms to form the equation.

The answer is:  

Split up the question into parts.

The square of a number:  

Three less than the square of a number:  

Is eleven:  

Combine the terms.

The answer is:  

Write the following sentence by parts.

A number squared:  

The difference of six and a number squared:  

Is four:  

Combine the parts to write an equation.

The answer is:  

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)