course Mth 163 assignment #004004.
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15:29:32 `questionNumber 40000 `q001. Note that this assignment has 4 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.
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RESPONSE --> f(x) = x^2 + 4 f(3) = 3^2 + 4 9+4 f(3)=13 (3,13) f(7) = 7^2 + 4 49+4 f(7)=53 (7, 53) f(-5) = -5^2 + 4 25+4 f(-5)=29 (-5,29) I plotted the points (3,13) (7, 53) (-5,29) and got parabola in the top two quadrants. confidence assessment: 2
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15:29:49 `questionNumber 40000 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.
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RESPONSE --> ok I see self critique assessment: 2
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15:38:22 `questionNumber 40000 `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.
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RESPONSE --> f(x) = x^2 + 4 f(a) = a^2 + 4 f(x+2) = x+2^2 + 4 simplify f(x+2) = (x^2+4x + 4)+4 f(x+2) = x^2+4x +8 f(x+h) = (x+h)^2+4 f(x+h) = (x+h)(x+h)+4 f(x+h) = x^2+2xh+h^2+4 f(x+h)-fx = x^2+2xh+h^2+4-x^2+4 use equations already found f(x+h)-fx =2xh+h^2 [f(x+h)-fx]/h= use last answer and divide by h 2xh+h^2/h=2x+h confidence assessment: 2
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15:38:34 `questionNumber 40000 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.
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RESPONSE --> I get it. self critique assessment: 2
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15:41:54 `questionNumber 40000 `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.
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RESPONSE --> f(x) = 5x + 7 f(x1) = 5(x1) + 7 f(x2) = 5(x2) + 7 [f(x2)-f(x1)]/ (x2-x1)= [5(x2+7)-5(x1+7)]/(x2-x1)= 5x2-5x1/x2-x1 Not sure if this is right, sort of guessed. confidence assessment: 2
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15:42:09 `questionNumber 40000 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.
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RESPONSE --> ok i see self critique assessment: 2
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15:43:18 `questionNumber 40000 `q004. If f(x) = 5x + 7, then for what value of x is f(x) equal to -3?
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RESPONSE --> fx) = 5x + 7 -3 = 5x + 7 -3+-7=5x -10/5=5x/5 -2=x confidence assessment: 2
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15:43:31 `questionNumber 40000 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.
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RESPONSE --> ok i see self critique assessment: 2
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