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Mathematics Practices
Exploration 156a: Rehearsal #1 for Test
Objective: Analyze polynomial functions and their rates of change.
Answer all of these questions on separate paper. You may draw graphs on this sheet where specified. 1. Let Plot the graph of f. Sketch the result here.
2. By synthetic substitution, show that 2 is a
zero of

For Problems 9–14, a freight train backs up, stops, and then goes forward. The displacement, kilometers, of its engine from a railroad crossing is given by
9. What is the average velocity of the train from 
Exploration 156b: Rehearsal #2 for Test
Objective: Analyze polynomial functions and their rates of change
1. Mr. X, the math teacher , is making up a test for his students. He wants them to find the particular equation of a cubic function, but all he will reveal about it is that for its three zeros, and , this is true: Find the particular equation for
. Plot the
graph, 2. One of the zeros of
is a real
number. Are the 6. Let . By
synthetic 
8. On this set of axes, sketch the graph of h.
9. At a double zero, the graph of a polynomial
function
10. What is its average velocity from
to 
Exploration 156c: Rehearsal #3 for Test, Date:
Annotated List
Objective: Analyze polynomial functions and their rates of change.
1. Find the particular equation of a polynomial function. a. From points, e.g., a cubic function containing the points (2, 7), (3, 34), (4, 91), and (5, 190). b. From zeros, e.g., a cubic function with leading coefficient 1 and zeros 5, 3, and 6. Write in factored form and then multiply and simplify . Confirm by graphing. c. From sums and products of zeros, e.g., sum= 1, product = 15, sum of pairwise products = 7. 2. Find zeros of a polynomial function. a. By graphing, e.g., Explain how you know that two of the zeros of are complex numbers. b. By synthetic substitution, e.g., Find the complex zeros using the quadratic formula. 3. Find discontinuities in a rational function . a. Vertical asymptotes, e.g.,

remove the removable discontinuity. Use the simplified equation to calculate the instantaneous velocity at exactly. d. Instantaneous rate by shortcut, e.g., let . Show that equals the instantaneous rate of change of at Explain how you can find the equation for from the equation for . e. Instantaneous rate graphically, e.g., the figure here shows the graph of from part a. Plot a line on the graph at the point with slope equal to the instantaneous rate of change of at that point. How is the line related to the graph?

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