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test 1 f07 - NCSU MA107 TEST 1 Fall 2007 2.2-2.8 3.1...

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Unformatted text preview: NCSU MA107 TEST 1 Fall 2007 2.2-2.8, 3.1, Regions bounded by curves - N0 Calculators, no cell phones, no PDA - Show all steps to work the problem neatly on your own paper. Circle your final answer. - No work No credit! Vx+5 x 1. Given f(x)= 4 pts. a. Find f(4) 6 pts b. State the domain off 2. Given f(x) = 3x2 — 5 lOpts 3. Find and simplify W, h :0 5 pts b. State any x-intercepts of f. 3. Given f(x) = 3x2 — 8x — 30 5 pts a. Find all x such that f(x) =5 5 pts b. Find f(-x) and simplify. 5 pts c. State the x-coordinate of the vertex of the graph off. 4 pts d. State the interval over the domain where f increases. 4. Given the function y = f (x) 5 pts a. Describe in words all the transformations that occur for h(x) =f(x-3)+2 5 pts b. Assume the point (0,1) is on the graph of y=f(x). Find its new coordinates on the graph of h(x)=f(x-3) +2. That is, find where (0,1) will be after all transformations. 5 pts a. Sketch the graph of y = f (x) = w/T and identify 3 key points. 5 pts b. Write the function g(x) whose graph is y = 1/; but is vertically stretched by a factor 9. <Continue on next page> 6. (10 pts) Make good sketches of f (x) = 3x — 4 and g(x) = x2 — 8 on the same coordinate system. Spread out units, label each curve. Shade the bounded region. Find the points (x, y) of intersection algebraically. 7. (10 pts.) Determine the quadratic function in either form y=ax2+bx+c or y=a(x—h)2+k with vetex (—3, 5) and y-intercept (0, -4). 8. (8 pts) Matt has 700 yards of fencing and wishes to enclose a rectangular area of length l and width w. a. Write the equation for the perimeter of this rectangular region. b. Express the area A of the rectangle as a function of w. (A(w)=?) 9. (9 pts) The monthly, in dollars, of a certain cellular phone plan is given by C (x)=0. 5 0x+3 0, where x is the number of minutes used on the phone. a. What is the cost if you talk for 100 minutes? b. Suppose your bill is $40. How many minutes did you use the phone? Write your correspondence address on your test. _ ., ~... ”__s... . ‘. -. . i $1x%)«.3(><+h) .s -'3(>< 32x1, whim?“ _ ____---”_‘l-_-_._w-.._¢._._ .:-..3x +éxézj3lzir ._._,_..-__ _ H.— x m», +3212 s—J—- [3.28: -:J _ ~-— —~~-~ MMw/é/ gru.f1§h£{fimMZ/%) 3 com ‘ ‘ \ll H qqlmlxwlm "u w“ :7: 4101:3116 .V-- “$.75: 74 +5: ' “ ...
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