1. Write a rational expression with at least one in the denominator and then analyze it using the following questions:a. Set your expression equal to 0. Does this expression have any solutions? Why, or why not?b. Set your expression equal to and graph the equation on a graphing utility or on your calculator. Are there any values that cannot be? Explain.c. How do the numbers and variables in your equation relate to the features of the graph?d. Identify the denominator of your expression; add 6 to the denominator only. How does the graph change?2. The math teacher and cheerleading coach have teamed up to help the students do better on their math test. The cheer coach, using dance move names for the positioning of their arms, yells out polynomial functions with different degrees.For each position the coach yells out, write the shape by describing the position of your left and right arm.a1. Constant Function:a2. Positive Linear Function:a3. Negative Linear Function:a4. Positive Quadratic Function:a5. Negative Quadratic Function:a6. Positive Cubic Function:a7. Negative Cubic Function:a8. Positive Quartic Function:a9. Negative Quartic Function:When it comes time to take the test not only do the students have to describe the shape of the polynomial function, you have to find the number of positive and negative real zeros, including complex. Use the equation below:b. Identify all possible rational zeros.c. How many possible positive real zeros are there? How many possible negative real zeros? How many possible complex zeros?d. Graph the polynomial to approximate the zeros. What are the rational zeros? Use synthetic division to verify these are correct.e. Write the polynomial in factor form.f. What are the complex zeros?

In this discussion, please answer the following question and post your response to the discussion board. Please keep in mind, in order to remain eligible for full credit in the discussion, you must, in addition to your initial reply, respond to at least two of your classmates’ or instructor’s posts.It does not take much observation for one to realize that the people of antiquity had a quite sophisticated knowledge of trigonometry. Many ancient architectural structures, for example, exhibit properties that make us wonder what exactly “the ancients” knew.Your task this week is to investigate and discuss in detail, anything from antiquity that you believe or suspect must have required a keen knowledge of trigonometry.( 200 words)