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The Second Quarterly Exam

The Second Quarterly Exam. Essential Question: Wait… didn’t we see this stuff before?. Question #1. Find all solutions: |x 2 + 8x + 14| = 2 Create two equations The solution is c. Question #2. Write 2 < x < 8 in interval notation

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The Second Quarterly Exam

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  1. The Second Quarterly Exam Essential Question: Wait… didn’t we see this stuff before?

  2. Question #1 • Find all solutions: |x2 + 8x + 14| = 2 • Create two equations • The solution is c

  3. Question #2 • Write 2 < x < 8 in interval notation • If an inequality has a line underneath it, we use braces; parenthesis without. • (2, 8]

  4. Question #3 • Solve the inequality and express your answer in interval notation: -15<-3x+3<-3 • [2, 6] • The answer is a

  5. Question #4 • Determine the domain of the function • The rule about domains are that they’re all real number except when taking square roots (not applicable) or dividing by 0. • To check the denominator, set it equal to 0. • x(x2 – 81) = 0 • x = 0 or x2 – 81 = 0 • x = 0 or x2 = 81 • x = 0 or x = +9 • The answer is a

  6. Question #5 & 6 • Use the vertical line test • Yeah… use the vertical line test • All of the graphs fail the vertical line test, except for a, which is your answer • Which function is in quadratic x-intercept form? • x-intercept form: a(x – s)(x – t) • The only one that fits that mold is b, which is your answer • Remember: • Transformation form: a(x – h)2 + k • Polynomial form: ax2 + bx + c • Your quarterly will ask you to identify one of the three

  7. Question #7 • Find the rule and the graph of the function whose graph can be obtained by performing the translation 3 units right and 4 units up on the parent function f(x) = x2. • Horizontal effects (right/left) are inside parenthesis. Vertical effects (up/down) are outside parenthesis. • Inside stuff works opposite the way you’d expect. Outside works normal. • f(x) = (x – 3)2 + 4 • The answer is c

  8. Question #8 • f(x) = x5 & g(x) = 4 – x. Find (g o f)(x) • Take x, plug it into the closest function (f) • f(x) = x5 • Take that answer, plug it into the next closest function (g) • g(x5) = 4 – x5 • The answer is c • Ignore the note about domains, but do make sure when the quarterly comes, you pay attention to order. • Answer a is (fg)(x) • Answer b is (f + g)(x) • Answer d is (f o g)(x)

  9. Question #9 • Find all solutions:

  10. Question #10 • Find all real solutions: • Real solutions? When numerator = 0 • x2 + x - 42 = 0 • (x - 6)(x + 7) = 0 • x = 6 or x = -7 • I’m only asking for real solutions, so just test your real solutions in the denominator to make sure they’re not extraneous (denominator = 0). • (6)2 + 16(6) + 63 = 195 (works) • (-7)2 + 16(-7) + 63 = 0 (extraneous) • Real solution: 6

  11. Question #11 • Solve the inequality and express your answer in interval notation: • Critical Points • Real solutions: 5 & -9 • Extraneous solution: 4 • Test the intervals • (-∞, -9] use x = -10, get -15/14 > 0 FAIL • [-9, 4) use x = 0, get 11.25 > 0 PASS • (4, 5] use x = 4.5, get -13.5 > 0 FAIL • [5, ∞) use x = 6, get 7.5> 0PASS • Interval solutions are [-9, 4) and [5, ∞)

  12. Question #12 • Find the selected values of the function • Check each input to decide which function it should be plugged into (top or bottom) • f(-1) [bottom function], -8 + 7(-1)2 = -1 • f(0) [top function], ⅓(0) = 0 • f(1) [top function], ⅓(1) = ⅓ • f(-1.9) [bottom function], -8 + 7(-1.9)2 = 17.27

  13. Question #13 • Tired of this question yet? • For parts a & b, find the valuealong the x-axis, and determine the y-value(find the output tomatch the input) • f(0) = 4 • f(-1) = 0 (use the closed dot) • Domain (x-values) = [-5, 5) • Range (y-values) = [-4, 4] (the peak counts)

  14. Question #14 • Determine the x-intercepts and vertex of the functionf(x) = x2 + 12x + 36 • x-intercepts are found using the quadratic equation, or factoring • (x + 6)(x + 6). There is only one x-intercept: -6 • The vertex is at • 1st coordinate: (-12)/2(1) = -6 • 2nd coordinate, plug in: (-6)2 + 12(-6) + 36 = 0 • Vertex is at (-6, 0)

  15. Question #15 • f(x) = 16 – x2, g(x) = 4 – x.Find (f – g)(x) and its domain • Subtract the second function from the first. Make sure to use parenthesis around the function. • [16 – x2] – [4 – x] (distribute the negative sign) • 16 - x2 – 4 + x (combine like terms, put in order) • -x2 + x + 12 • Domain of f is all real numbers. Domain of g is also all real numbers. The domain of the added function is all real numbers.

  16. Question #16 • Find the difference quotient: 2x2 – 3x – 8Function using (x+h) – function using x

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