A+ Work

1.         For each of the following polynomials, answer the following questions:

            a.         How many solutions does P(x) have?

            b.         What are the solutions?

            c.         What is the multiplicity of each zero?

            d.         How many of the zeroes are real, and how many are complex?

                        i.          P(x) = 5x⁵ – 10x⁴ – 15x³

                        ii.         P(x) = 4x³ – 5x² + 3x

2.         Graph the following rational functions, by following the given steps:

            a.         Factor completely

            b.         Find x-intercepts

            c.         Find y-intercepts

            d.         Find Vertical Asymptotes

            e.         Find Horizontal Asymptotes

            f.          Check behavior around the Vertical Asymptotes

            g.         Graph

                        i.           

                        ii.         

3.         Graph

                        a.  

                        b.   

4.         Find the exponential function, f(x) = a^x with the given graph:

5.         Evaluate the following expressions:

            a.   

            b.  

            c.   

6.         Solve the following equations:

            a.   

            b.  

            c.   

7.         Use the laws of logarithms to expand completely:

            a.   

            b.  

8.         a. Express in exponential form and explain how you can estimate the answer.

            b. Use the change of base formula to evaluate the following to three decimal                    places.

            a. Exponential form: 5^x = 100

            b.  Using the change of base formula gives:

9.         Evaluate the following: If f(x) = 3^{2x – 1} and g(x) = 2e^0.04x

            a. f(1.2)

            b.  g(-0.5)

            c.  f(0) + g(0)

10.       The stray cat population in a small town grows exponentially. In a certain year,   the town had 30 stray cats, with a relative growth rate of 15% per year.

            a.  Find a function that models the stray cat population n(t) after t years.

            b.  Find the projected population after 4 years.

            c.  Find the number of years required for the stray cat population to reach 1,000

            cats.

11.       P(x, y) is on the unit circle in Q IV. If , find y.

12.       Find all six trigonometric value of t for:

            a. t = -3π/2

            b. t = 2π/3

13.       Find the exact values of:

            a.  

            b.   

            c.   

            d.   

            e.   

14.       Find 2 angles co-terminal with:

            a. 315º, express your answer in degrees

            b. 5π/6, express your answer in radians

15.       a.  Express in degrees: -3π/8

            b.  Express in radians: 25º

16.       Find the amplitude, period, phase shift, reflections, and 5 critical points. Graph             one complete period of:

            a. 

            b.  

            c.  

17.       Find the missing side:

18.       A tree casts a shadow on the ground. If the shadow is 7.5 feet, and if the angle             from the end of the shadow to the top of the tree is 32º, find the height of the tree.

19.       A person pulls on a spring and charts its height for 10 seconds. The graph is             below:

            positive?

            a. Which trigonometric function would you use to model this graph? Negative or            

            b.  What is the period of this function?

            c.  What is the amplitude?

            d. What is the equation that you would use to model the above graph?