class 050919

class 050921

Briefly, to take your test go to the Learning Lab, go to a computer and do the following:

Go to your homepage at http://vhmthphy.vhcc.edu/ and click on Tests.
Print off the test.
Get it signed by the attendant.
Take it in the room to which the attendant directs you.
Hand it to the attendant.

No calculators are to be used for the following:

1. (2 minute time limit)

Make tables and sketch graphs of y = f(x) for each of the following functions, using the basic points for that function.

f(x) = x^-2

f(x) = 2^x

2. (2 minute time limit)

The graph below represents water depth in cm vs. clock time in seconds.

Based on the graph

Estimate the average rate of change of depth with respect to clock time between t = 10 and t = 30.
Estimate the average rate of change of depth with respect to clock time between t = 15 and t = 25.

3. For the function y = f(t) = 2 t^2 - 3, what is the value of ( f(t2) - f(t1) ) / ( t2 - t1) for t1 = 1 and t2 = 3?

questions for 050919

Simple Power Function Form: y = A x ^ p.

Quadratic Function Form: y = a t^2 + b t + c

Quadratic Function Characteristics: Vertex on axis of symmetry at t = -b / (2 a). Move 1 unit right or left and vertical displacement is a units.

Given any function y = f(t) then

to find y for given t, evaluate f(t)
to find the zeros of f(t) solve the equation f(t) = 0.
to find t that yields y solve the equation y = f(t) for t.

Given basic function y = f(x), then

y = A f(x) vertically stretches the graph by factor A
y = f(x - h) horizontally shifts the graph h units
y = f(x - h) + k vertically shifts the graph k units.
y = A f(x-h) + k does all three.

The behavior of the function is easily traced by observing the effects of these transformations on the function's basic points.

Time and Date Stamps (logged): 10:12:00 09-19-2005 °¯Ÿ°±Ÿ¯¯¯¸Ÿ°¸Ÿ±¯¯´

Precalculus I Major Quiz

Test should be printed using Internet Explorer. If printed from different browser check to be sure test items have not been cut off. If items are cut off then print in Landscape Mode (choose File, Print, click on Properties and check the box next to Landscape, etc.).

Write on ONE SIDE of paper only
If a distance student be sure to email instructor after taking the test in order to request results.

Name and Signature of Student _____________________________

Signed by Attendant, with Current Date and Time: ______________________

If picture ID has been matched with student and name as given above, Attendant please sign here: _________

Instructions:

Test is to be taken without reference to text or outside notes.
Graphing Calculator is allowed, as is blank paper or testing center paper.
No time limit but test is to be taken in one sitting.
Please place completed test in Dave Smith's folder, OR mail to Dave Smith, Science and Engineering, Va. Highlands CC, Abingdon, Va., 24212-0828 OR email copy of document to dsmith@vhcc.edu, OR fax to 276-739-2590. Test must be returned by individual or agency supervising test. Test is not to be returned to student after it has been taken. Student may, if proctor deems it feasible, make and retain a copy of the test..

Directions for Student:

Completely document your work.
Numerical answers should be correct to 3 significant figures. You may round off given numerical information to a precision consistent with this standard.
Undocumented and unjustified answers may be counted wrong, and in the case of two-choice or limited-choice answers (e.g., true-false or yes-no) will be counted wrong. Undocumented and unjustified answers, if wrong, never get partial credit. So show your work and explain your reasoning.
Due to a scanner malfunction and other errors some test items may be hard to read, incomplete or even illegible. If this is judged by the instructor to be the case you will not be penalized for these items, but if you complete them and if they help your grade they will be counted. Therefore it is to your advantage to attempt to complete them, if necessary sensibly filling in any questionable parts.
Please write on one side of paper only, and staple test pages together.

Test Problems:

Problem Number 1

Problem: Obtain a quadratic depth vs. clock time model if depths of 80.93887 cm, 68.64622 cm and 62.12207 cm are observed clock times t = 12.32081, 24.64162 and 36.96243 seconds.

Problem: The quadratic depth vs. clock time model corresponding to depths of 80.93887 cm, 68.64622 cm and 62.12207 cm at clock times t = 12.32081, 24.64162 and 36.96243 seconds is depth(t) = .019 t² + -1.7 t + 99. Use the model to determine whether the depth will ever reach zero.

Problem Number 2

Problem: If we apply a vertical stretch by factor .79 then a vertical shift of -2.04 units to the graph of the basic exponential function y = 2^x, what is the algebraic form of the function obtained? Sketch a graph of this new function, and show that the graph is different than that obtained if the vertical shift is performed before the vertical stretch.

Problem: At clock times t = 12, 24, 36 and 48 seconds, the depth of water in a uniform cylinder was observed to be 58.224, 44.496, 36.816 and 35.184 cm. At what average rate does the depth change during each of the three time intervals? Predict, based on your calculated rates, what the next average rate would be. Based on your prediction, what will be the depth at t = 60 seconds?

Problem Number 3

Sketch a graph of y = x^2, from x = -3 to x = 3. Then sketch a graph of y = .25 x^2 over the same domain.

By what factor do we vertically stretch the first graph to obtain the second?
What are the three basic points of the first graph (i.e., the vertex and the points 1 unit to the right and left of the vertex)?
What are the three basic points of the second graph?

Sketch the second graph shifted 1.75 units in the x direction and .75 units in the y direction.

What are the three basic points of this graph?

If f(x) = x^2, then what are

f(x- 1.75), f(x) + .75, .25 f(x) and .25 f(x- 1.75) + .75?

Problem Number 4

If f(x) = x², give the vertex and the three basic points of the graphs of f(x--.25), f(x) - .35, 2 f(x) and 2 f(x--.25) + .35. Quickly sketch each graph.

If water depths of -66.4, -108, -136.2 and -150.9 cm are observed at clock times 51.8, 77.7, 103.6 and 129.5 sec, then at what average rate does the depth change during each time interval?

Sketch a graph of this data set and use a sketch to explain why the slope of this graph between 77.7 and 103.6 sec represents the average rate at which depth changes during this time interval.

Problem Number 5

At clock time t = 12 sec the depth of water in a container is 60 cm, while at clock time t = 34 sec the depth is 30 cm. Plot the corresponding points on a graph of depth vs. clock time and determine the slope of the straight line segment connecting these points. Explain why this slope represents the average rate at which the water depth changes over this time interval.

For the quadratic function y = f(t) = .018 t² + -2.18 t + 84, determine the average rate of change of y with respect to t, between clock times t = 34 and t = 40.

questions etc.