MTH1014 Quiz 4

Spring 2013
Herbert J. Bernstein ( )

MTH1014 Quiz 4
Spring 2013

 		 

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This is quiz 4 to be taken by Friday, 1 March 2013. It should take you between half an hour and 2 hours to answer the following questions. You should do this quiz after doing the rest of assignment 4'.

  <==== Do this AFTER you've answered all the questions

You probably DON'T want to do this ===>  

Please fill in the following information:

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Please answer the following questions on this form (or on a paper copy of this form).


  1. Carefully, and in detail, using words, no picture, explain what a relation is and when a relation represents a function. Be sure to define and discuss both the domain and the range of a function. Give a specific example of a function, identifying the range and domain of that function

  2. Carefully and in detail, using words, no picture, explain how to determine of an equation represents a function. Give two examples, one of an equation that does not represent a function, and one of an equation that does represent a function.

  3. If the function f(x) has the equation f(x) = 3*x2 - 2*x + 5, what are the values of f(0), f(1), f(2), f(3) and f(4).

  4. Carefully and in detail, without actually drawing anything, explain the vertical line test, and given using the the graph of a circle and the graph of a parabola, give an example of a graph that is not the graph of a function according to the vertical line test and an example of a graph that may be the graph of a function according to the vertical line test.

  5. Carefully and in detail, without actually drawing anything, just using words, explain what it means to say that a function is an odd function, to say that a function is an even function and give an example of a function that is an odd function and an example of a function that is an even function.

  6. Using a graphing calculator or a graphing program or a piece of scrap paper, make yourself a graph of the function f(x) = |x3+x2+x+1| and report as accurately as you can the intervals within which f(x) is increasing and the intervals within which f(x) is decreasing. Dont forget to pay attention to the absolute value in this function.'

  7. Using a graphing calculator or a graphing program or a piece of scrap paper, make yourself a graph of the function f(x) = x2-x+1 and using the graph and as much algebra as you can report the average rate of change of f from -5 to 5 and find the equation of the secant line from (-5,f(-5)) to (5,f(5)). Be sure to check your agebraic results against your graph results and vice-versa.

  8. Carefully and in detail, using words, not a picture, describe the graphs of the constant function and the reciprocal function, giving the range and domain for each function. If you draw the graph of the constant function for the constant 0 on the same graph as the graph of the reciprocal function, where do these two graphs intersect.

  9. Carefully and in detail, using words, not a picture, describe the graphs of the square root function and the cube root function and say ways in which they are similar and ways in which they are different. Give the domain and range for each function.

  10. Carefully and in detail, using words, not a picture, describe the graphs of the square function and the cube function and say ways in which they are similar and ways in which they are different. Give the domain and range for each function.

  11. Carefully and in detail, using words, not a picture, describe the graphs of the identity function and the absolute value function saying where they are the same and where they are different. Give the domain and range for each function.

  12. Suppose we try to define y as a function of x using the equation x*y = 10. Using words, not a picture, give the domain and range for this function and the values of y for x= -5, -4, -2, -1, 1, 2, 4 and 5

  13. Consider a function f pieced together from f(x) = 0 if |x| ≤ 1, f(x) = |x|-1 if 1 < |x| < 2, f(x) = 1, otherwise. Give the domain of f, the range of f and the values of f(-5), f(-4), f(-3), f(-2), f(-1), f(0), f(1), f(2), f(3), f(4), f(5)

  14. Carefully and in detail, without drawing anything, just using words, explain the use of vertical shifts, horizontal shifts, compressions, stretches and reflections to graph functions. To clarify your explanation, using tables of numbers, rather than graphs, give a detailed example based on the absolute value function f(x) = |x|

  15. Consider the graph of y(x) = x2+1. Suppose for each value of x, you draw a circle around the origin that just touches the point (x,y(x)). Call the area of that circle A(x). Write an equation for A(x) and compute the values of A(0), A(-1), A(1), A(2) and A(-2)

  <==== Do this AFTER you''ve answered all the questions

You probably DON'T want to do this ===>  

Revised 28 February 2013