Make up two polynomial functions, f of x and g of x. f of x should be of degree 3 or higher. g of x should be of degree 4 or higher.
Find f of 3 in each of the three ways: substitution, remainder theorem (synthetic division), and long division. You should get the same answer three times for f of 3.

Find g of negative 2 once using your choice of the three methods.
Organize your four calculations in an orderly manner. (Images will need to be provided in your post.)
A. Post your polynomials, f of x and g of x, and submit screenshots of your organized calculations.

Answer the following questions:

Why did you choose the method you used to solve g of negative 2?
Can you think of any other ways (other than the three used here) to evaluate a function?
Can you come up with and explain a way to check your answer?
Challenge: Can you explain why the remainder theorem works?

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).