1. Consider the piecewise function
a. Find f (-2)
b. Find f (0)
2. A graph of y = f(x) follows. No formula for f is given.
Which graph (A, B, C, or D) represents the graph of y= f(x - 1) -1?
EXPLAIN YOUR CHOICE.(Grid supplied for scratch work; You are NOT required to submit your own graph)
Explain why you chose your answer.
a. Evaluate f (-x). How does the graph of f (x) compare to the graph of f (-x)?
b. Evaluate -f (x). How does the graph of f (x) compare to the graph of -f (x)?
c. Evaluate -f (-x). How does the graph of f (x) compare to the graph of -f (-x)?
3. Let f (x) = x3 - 2
4. Let f (x) = x3 - 7x. Determine if this function is even, odd or neither. Explain/Show work.
5. The graph of the function y = f (x) is pictured below.
(a) State the domain of the piecewise function.
(b) State the range of the piecewise function.
(c) State the value of f(-3).
(d) State the interval(s) on which the function is increasing. That is, for what x-values is the function increasing?
(e) List the local minimums, if any exist.
(f) The piecewise function has 4 pieces. Write the formula for just ONE PIECE of this piecewise function. (You choose the piece you prefer. No explanation required)
f(x) = ___________________ for __________________ (state the x-values associated with your piece).
6a. Find the point-slope form of the line which passes through: P(-3,1) and Q(3,-5).
6b. Find the slope-intercept form of the line that passes through R(-6,-1) and S(2,-13).
7. In 2000, U.S. farmers received an average price of $157 per ton for shelled corn. In 2008, they received an average price of 84.60 per ton.
a. What is the average rate of change in price of shelled corn over this time period?
b. Interpret the average rate of change in the context of this problem.
c. Find the linear function P(x) that models the change in the price of shelled corn over this time period.
d. Based on your linear model form 7c, what is the predicted price of shelled corn for 2015?
8. Given the function f (x) = ¦x + 1¦- 2.
a. Sketch the graph of f. You may use the axis provided.
b. State the domain and range in interval notation.
c. State the interval(s) where the function is decreasing. Use interval notation.
d. Find any absolute extrema.
9. A study was conducted by students in a Psychology class where they asked classmates to study a list of nonsense words for various amounts of time and then to try to recall as many words from the list as possible 30 minutes later. One student conducted the experiment with four students. Their respective times studying the words (Time) and the number of words recalled 30 minutes later (Words) is displayed below.
|
Time
|
3
|
5
|
8
|
10
|
|
Words
|
7
|
8
|
14
|
18
|
The student graphed the data and thought that a linear equation would best model her data.
She then entered the data into a calculator and ran a Linear Regression on the data. A screen shot of her results are below.
a. Based on this analysis, was she justified in using a linear model? Justify your answer using the results above.
b. What is the slope of the regression line and interpret it in the context of her experiment.
c. Write the equation of the regression line.
d. Based on the regression line how many nonsense words would she expect someone to remember if they were given 15 minutes to study? Show work to support your answer.
Bonus: A sales man gets a salary $1000 a month a 5% commission on all sales he makes that month.
a. Write the equation S(x) that represents the salesman's salary for any month.
b. If the salesman has a total of $30,650 in sales for this month, what would his monthly salary be?