Test 1, Sections 1-1 to 1-3



Test 1, Sections 1-1 to 1-3 Form B

Objective: Identify and transform functions and their graphs.

Part 1: No calculators allowed (1–8)

1. You pour a cup of freshly brewed coffee but forget to drink it. As the coffee sits there, its temperature depends on the number of minutes that have passed since you poured it.

2. What type of function has a graph like the one you sketched in Problem 1?

3. If [pic] what type of function is f?

4. If [pic] what type of function is f?

5. The graph shows a polynomial function. The domain of the function is (3 ( x ( 2.3. What is the range of the function?

[pic]

6. What type of function has a graph like this?

[pic]

7. The graph of f(x) is shown. Sketch the graph of

function g, a horizontal dilation by a factor of [pic] Write g(x) in terms of f(x).

Equation: __________________________________

[pic]

8. If g(x) ’ f(x) −7, describe the transformation, and sketch the graph of function g.

Verbally: __________________________________

[pic]

(Hand in this page to get the rest of the test.)

Test 1, Sections 1-1 to 1-3 continued Form B

Part 2: Graphing calculators allowed (9–21)

9. The graph shows − x2 + 2x + 3 plotted in the domain −1 ( x ( 4. Plot this graph using a friendly window. Divide by the Boolean variable (x ( −1 and x ( 4) to get the domain shown. Check your graph with your instructor.

[pic]

For Problems 10–14, identify the transformation of the graph of f (dashed) to get the graph of g (solid). Plot the graph of g on your grapher and state whether it checks.

10.

[pic]

11.

[pic]

12.

[pic]

13.

[pic]

14.

[pic]

Drinking Cup Problem (15–20): Disposable drinking cups can be stacked so that one cup fits inside the next. A stack of 5 cups is 9.5 cm tall. Each cup is 7.5 cm tall.

15. Make a sketch showing what a stack of 5 cups would look like.

16. How many centimeters are added to the stack for each cup? Show how you get your answer.

17. Let f(n) be the height in centimeters for a stack of n cups. Write an equation for f(n) in terms of n.

18. What type of function did you write in Problem 17?

19. Based on your equation in Problem 17, how tall would a stack of 15 cups be?

20. The manufacturer packages the cups in boxes 32.2 cm tall. Each box holds a single stack of cups. What is the greatest number of cups that can be put in a stack without exceeding the 32.2 cm? Show how you get your answer.

21. What did you learn as a result of taking this test that you did not know before?

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