course Mth 163
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18:15:10 `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 --> To find f (3), f (7), and f (- 5) you substitute each of the three coefficients into function given. After this is done we find that f (3) = 13, f (7) = 53, and f (- 5) = 29. The points to put onto a graph, would be ( 3, 13), ( 7, 53), ( -5, 29). This graph comes out to be a parabola passing through the points, since f (x) is a quadratic formula, where a = 1, b = 0, and c = 4. self critique assessment: 2
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18:21:02 `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 --> The symbolic expression for f (a) is f(a) = a^2 + 4. Then the expression for f (x+2) is f(x+2) = (x + 2)^2 + 4. This expression can be expanded to either (x^2 + 4 x + 4) + 4 or x^2 + 4 x + 8. The next expression is expressed as f(x+h) = (x + h)^2 + 4 = x^2 + 2 h x + h^2 + 4. To find the solution to f(x+h) - f(x) we use what we found for f (x) and f (x+h). confidence assessment: 2
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18:27:05 `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 --> The symbolic expression for f (x1) is 5 * x1 + 7, the f (x2) symbolic expression is 5 * x2 + 7. The symbolic expression for [f(x2) - f(x1) ] / ( x2 - x1 ) is 5 ( x2 - x1 ) / ( x2 - x1 ) = 5. You obtain this solution by substituting both f (x1) and f (x2) into the function, then once you get that answer you can factor out the 5 and you get the obtained solution. confidence assessment: 2
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18:29:40 `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 --> You simply substitute -3 into the equation for f (x), where you get -3 = 5 x + 7. Then, you simply solve the equation by subtracting 7 from both sides and then dividing both sides by 5. When this is done the answer obtained for the equation is x = -2. confidence assessment: 3
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