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If your solution to stated problem does not match the given solution, you should self-critique per instructions at

 

   http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

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Your solution, attempt at solution.  If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it.  This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

 

004.

 

Question:  `q001.    Note that this assignment has 7 questions

 

If f(x) = x^2 + 4, then find the values of the following:  f(3), f(7) and f(-5).  Plot the corresponding points on a graph of y = f(x) vs. x.  Give a good description of your graph.

 

 

Your solution: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Confidence Assessment:

Given Solution: 

f(x) = x^2 + 4.  To find f(3) we replace x by 3 to obtain

 

f(3) = 3^2 + 4 = 9 + 4 = 13.

 

Similarly we have

 

f(7) = 7^2 + 4 = 49 + 4 = 53 and

 

f(-5) = (-5)^2 + 9 = 25 + 4 = 29.

 

Graphing f(x) vs. x we will plot the points (3, 13), (7, 53), (-5, 29).  The graph of f(x) vs. x will be a parabola passing through these points, since f(x) is seen to be a quadratic function, with a = 1, b = 0 and c = 4.

 

The x coordinate of the vertex is seen to be -b/(2 a) = -0/(2*1) = 0.  The y coordinate of the vertex will therefore be f(0) = 0 ^ 2 + 4 = 0 + 4 = 4.  Moving along the graph one unit to the right or left of the vertex (0,4) we arrive at the points (1,5) and (-1,5) on the way to the three points we just graphed.

 

 

Self-critique (if necessary):

 

 

 

 

 

 

 

 

 

 

Self-critique rating:

Question:  `q002.  If f(x) = x^2 + 4, then give the symbolic expression for each of the following:  f(a), f(x+2), f(x+h), f(x+h)-f(x) and [ f(x+h) - f(x) ] / h.  Expand and/or simplify these expressions as appropriate.

 

 

Your solution: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Confidence Assessment:

Given Solution: 

If f(x) = x^2 + 4, then the expression f(a) is obtained by replacing x with a:

 

f(a) = a^2 + 4.

 

Similarly to find f(x+2) we replace x with x + 2:

 

f(x+2) = (x + 2)^2 + 4, which we might expand to get (x^2 + 4 x + 4) + 4 or x^2 + 4 x + 8. 

 

To find f(x+h) we replace x with x + h to obtain

 

f(x+h) = (x + h)^2 + 4 = x^2 + 2 h x + h^2 + 4.

 

To find f(x+h) - f(x) we use the expressions we found for f(x) and f(x+h):

 

 f(x+h) - f(x) = [ x^2 + 2 h x + h^2 + 4 ] - [ x^2 + 4 ] = x^2 + 2 h x + 4 + h^2 - x^2 - 4 = 2 h x + h^2.

 

To find [ f(x+h) - f(x) ] / h we can use the expressions we just obtained to see that

 

 [ f(x+h) - f(x) ] / h = [ x^2 + 2 h x + h^2 + 4 - ( x^2 + 4) ] / h = (2 h x + h^2) / h = 2 x + h.

 

You should have written these expressions out, and the following should probably be represented on your paper in form similar to that given here:

 

Self-critique (if necessary):

 

 

 

 

 

 

 

 

 

 

Self-critique rating:

Question:  `q003.  If f(x) = 5x + 7, then give the symbolic expression for each of the following:  f(x1), f(x2), [ f(x2) - f(x1) ] / ( x2 - x1 ).  Note that x1 and x2 stand for subscripted variables (x with subscript 1 and x with subscript 2), not for x * 1 and x * 2.  x1 and x2 are simply names for two different values of x.  If you aren't clear on what this means please ask the instructor.

 

 

Your solution: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Confidence Assessment:

Given Solution: 

Replacing x by the specified quantities we obtain the following:

 

f(x1) = 5 * x1 + 7,

 

f(x2) = 5 * x2 + 7,

 

[ f(x2) - f(x1) ] / ( x2 - x1) = [ 5 * x2 + 7 - ( 5 * x1 + 7) ] / ( x2 - x1) = [ 5 x2 + 7 - 5 x1 - 7 ] / (x2 - x1) = (5 x2 - 5 x1) / ( x2 - x1).

 

We can factor 5 out of the numerator to obtain

 

5 ( x2 - x1 ) / ( x2 - x1 ) = 5.

 

Compare what you have written down with the expressions below:

 

 

 

Self-critique (if necessary):

 

 

 

 

 

 

 

 

 

 

Self-critique rating:

Question:  `q004.  If f(x) = 5x + 7, then for what value of x is f(x) equal to -3?

 

 

Your solution: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Confidence Assessment:

Given Solution: 

If f(x) is equal to -3 then we right f(x) = -3, which we translate into the equation

 

5x + 7 = -3.

 

We easily solve this equation (subtract 7 from both sides then divide both sides by 5) to obtain x = -2.

 

Self-critique (if necessary):

 

 

 

 

 

 

 

 

 

 

Self-critique rating:

 

 

 

If you understand the assignment and were able to solve the previously given problems from your worksheets, you should be able to complete most of the following problems quickly and easily.  If you experience difficulty with some of these problems, you will be given notes and we will work to resolve difficulties.

 

 

 

Question:  `q005.   If f(x) = 3 x + 2 then what are the values of f(3),f(x+3), 3 f(x) and f(x+h) - f(x)?



 

Your solution: 

 

 

 

Confidence rating:

 

 

 

Question:  `q006.  If f(x) = 3 x + 2 then what is the value of f(0)? Faor what value(s) of x do we have f(x) = 0?

 

Your solution: 

 

 

 

Confidence rating:

 

 

Question:  `q007.  Evaluate the expression

for the function f(x) = 2 ( x - 3 ) + 5. 

Your solution: 

 

 

 

Confidence rating:

 

 

Self-critique rating:

 

 

 

 

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