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- Write a rule for a fifth-degree polynomial f that has
- x-intercepts -4, -3, and 2
- with f(x) > 0 when x < 2.
- Let
| f(x) = | (2x + 10)(25 - x)
(x + 30)2 |
- Find the intercepts and the asymptotes for the graph of f.
- Draw the graph of f. Your graph should include a dotted line for each asymptote and all intercepts (graph and asymptotes) should be labeled with their vertices.
- Let p(x) = - (2x - 20)3 + 6(2x - 20)2(4 - x)
- Find all of the factors of p and write p as a product of those factors. (Do not expand the products; factor!)
- Find the x-intercept(s) and the y-intercept for the graph of p. Answers should be clearly labeled.
- Draw a graph of p. Your graph should have all intercepts labeled with their values and units clearly marked on the x-axis.
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- Simplify each of the following. Your answers should not include negative exponents, radicals (such as a square root or fourth-root) or approximations.
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- 1000log (30 p)
- Write 3 [log (x + 2) - 2 log (x - 1)] as a single logarithm. Use only positive exponents.
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- Solve the equation (exact values): log6 x + log6 (x + 9) = 2
- For each of the following equations, name and draw the graph. Your graph should be clearly labeled with the coordinates of every vertex and should show any asymptote with a dotted line. Intercepts should be labeled with their values or coordinates.
- 25x2 + 9y2 = 900
- x + 4y2 = 4
- 25x2 - 9y2 = 900
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- Draw the graph of an exponential function that goes through the points (0, 200) and (20, 5). Write a function that could have the graph.
- Find all real solutions for the equation e4x - e2x = 20.
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- Let s = ln x and t = ln y. Write the expression ln (x y2)/sqrt(e) ) in terms of s and t. (For example, 3 ln x + 4 ln y = 3s + 4t ). Your answer should not include "ln"
- Let f(x) = log3 (x + 9).
- What is the domain of f?
- Draw the graph of f. Label intercepts with their values. Show any asymptote with a dotted line and label it with its equation or intercept value.
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