# Essential Question: Wait… didn’t we see this stuff before?

## Presentation on theme: "Essential Question: Wait… didn’t we see this stuff before?"— Presentation transcript:

Essential Question: Wait… didn’t we see this stuff before?

 Find all solutions: |x 2 + 8x + 14| = 2  Create two equations  The solution is c

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

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

 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(x 2 – 81) = 0  x = 0orx 2 – 81 = 0  x = 0orx 2 = 81  x = 0orx = +9  The answer is a

5) 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 6) 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: ax 2 + bx + c  Your quarterly will ask you to identify one of the three

 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) = x 2.  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

 f(x) = x 5 & g(x) = 4 – x. Find (g o f)(x)  Take x, plug it into the closest function (f) f(x) = x 5  Take that answer, plug it into the next closest function (g) g(x 5 ) = 4 – x 5  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)

 Find all solutions:

 Find all real solutions:  Real solutions? When numerator = 0 x 2 + 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

 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 > 0FAIL  [-9, 4)use x = 0, get 11.25 > 0PASS  (4, 5]use x = 4.5, get -13.5 > 0FAIL  [5, ∞)use x = 6, get 7.5 > 0PASS  Interval solutions are [-9, 4) and [5, ∞)

 Find the selected values of the function  Check each input to decide which function it should be plugged into (top or bottom) a) f(-1) [bottom function], -8 + 7(-1) 2 = -1 b) f(0) [top function], ⅓ (0) = 0 c) f(1) [top function], ⅓ (1) = ⅓ d) f(-1.9) [bottom function], -8 + 7(-1.9) 2 = 17.27

 Tired of this question yet?  For parts a & b, find the value along the x-axis, and determine the y-value (find the output to match 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)

 Determine the x-intercepts and vertex of the function f(x) = x 2 + 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  1 st coordinate: (-12)/2(1) = -6  2 nd coordinate, plug in: (-6) 2 + 12(-6) + 36 = 0  Vertex is at (-6, 0)

 f(x) = 16 – x 2, 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 – x 2 ] – [4 – x] (distribute the negative sign)  16 - x 2 – 4 + x (combine like terms, put in order)  -x 2 + 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.

 Find the difference quotient: 2x 2 – 3x – 8 Function using (x+h) – function using x