Revision for Midterm 1 PDF

Revision for Midterm 1 L1.1: Key Features of Functions L1.2: Transformations of Functions L1.3: Piecewise Functions L1.4 Arithmetic Sequences L2.1 Vertex form of Quadratic Functioms L1.1 Key features of functions Domain and range x and y intercepts Positive...

Revision for Midterm 1 L1.1: Key Features of Functions L1.2: Transformations of Functions L1.3: Piecewise Functions L1.4 Arithmetic Sequences L2.1 Vertex form of Quadratic Functioms L1.1 Key features of functions Domain and range x and y intercepts Positive and Negative Increasing and Decreasing Example 1: identify the key features of the following function - Domain: - Range: - x-intercepts: - y-intercept: 2 - Positive : - Negative : - Increasing: - Decreasing: Example 2: identify the key features of the following function - Domain: - Range: - x-intercepts: - y-intercept: -8 - Positive : - Negative : - Increasing: - Decreasing: L1.2 Transformations of Functions Vertical and Horizontal Translation L1.2 Reflection g(x)=-f(x) g(x)=f(-x) reflection reflection across x- across y- axis axis L1.2 Dilation  Write the equation of the graph shown………………… 𝟐 𝒇 ( 𝒙 ) =( 𝒙 − 𝟒) L.O: I can Write an equation of a transformed function.  Function g can be thought of as a translated (shifted) version of f(x) = 𝟐 Write the equation L.O: I can Write an equation of a transformed function. ( 𝒙 +𝟓) for g(x).  The parabola f(x) = is shifted up by 4 units and to the right by 3 units Write the equation for g(x). 𝟐 ( 𝒙 − 𝟑) +𝟒 L.O: I can interpret the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative). L.O: I can Write an equation of a transformed function.  The parabola f(x) = is shifted down by 6 units and to the right by 5 units Write the equation for g(x). 𝟐 ( 𝒙 − 𝟓) − 𝟔 L.O: I can interpret the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative). L.O: I can Write an equation of a transformed function.  The parabola f(x) = is shifted up by 4 units and to the right by 3 units Write the equation for g(x). 𝟐 ( 𝒙 − 𝟑) +𝟒 L.O: I can interpret the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative). L.O: I can Write an equation of a transformed function.  Function g can be thought of as a translated (shifted) version of f(x) =. Describe the translation then write the equation of g(x). 𝟐 Write the equation ( 𝒙 − 𝟑) − 𝟒 for L.O: I can g(x). Write an equation of a transformed function.  The parabola is shifted up by 5 units and to the left by 3 unit. What is the equation of the new parabola? 𝟐 𝒚 =( 𝒙 +𝟑)+𝟓 L.O: I can interpret the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative). L.O: I can Write an equation of a transformed function. Example 2: Describe how the graph of n(x) = 2x2 is related to the graph of f(x) = x2. A. n(x) is compressed vertically from f(x). B. n(x) is translated 2 units up from f(x). C. n(x) is stretched vertically from f(x). D. n(x) is stretched horizontally from f(x). Example 4: Describe how the graph of 12 b(x) = x__ – 4 is related to the graph of f(x) = x2. 2 A. b(x) is stretched vertically and translated 4 units down from f(x). B. b(x) is compressed vertically and translated 4 units down from f(x). C. b(x) is stretched horizontally and translated 4 units up from f(x). D. b(x) is stretched horizontally and translated 4 units down from f(x). Describe the following transformation: g(x)= g(x) is vertically stretched of f(x) by a factor of 2 g(x) is a vertical translation of f(x) by 5 units up g(x) is a horizontal translation of f(x) by 4 units to the right L 1.3 Piecewise function Graphing piecewise functions Domain: (- Range: (- Graphing piecewise functions Domain: (- Range: (- Graphing piecewise functions Domain: (- Range: (- Graphing piecewise functions Domain: (- Range: (-)  Lesson 1.3: Piecewise-defined Write a piecewise-defined rule Functions from a graph Lesson 1.3: Piecewise-defined Functions Piecewise function-problem solving Piecewise function-problem solving Piecewise function-problem solving GYM MEMBERSHIP PRICING  Less than 1 month – 150 admission fee  1 to 2 months – 200 AED per month + 50 AED admission fee  More than 2 months – 150 AED per month + 50 AED admission fee 𝑓 ( 𝑥 ) =¿ 150 200 𝑥 +50 150𝑥 +50 L1.4 Arithmetic Sequences L1.4 Arithmetic Sequences 1. Which of the following is an arithmetic sequence with a common difference of −2? 𝖠. 2, −4, 8, −16, 32, … 𝖡. −2, −4, −8, −16, −32, … 𝖢. 8, 6, 4, 2, 0, … 𝖣. −8, −6, −4, −2, 0, … L1.4 Arithmetic Sequences 𝒂𝒏 =𝟏𝟎 −𝟒(𝒏 −𝟏) L1.4 Arithmetic Sequences 𝒂𝒏 { 𝟗 , 𝒏=𝟏 𝒂𝒏 − 𝟏 +𝟔 , 𝒏 >𝟏 𝒂𝒏 { 𝟏. 𝟓 , 𝒏=𝟏 𝒂𝒏 − 𝟏 +𝟎. 𝟕𝟓 , 𝒏> 𝟏 𝒂𝒏 { 𝟕 , 𝒏=𝟏 𝒂𝒏 − 𝟏 − 𝟕 , 𝒏>𝟏 𝒂𝒏 =𝟏.𝟓+𝟎.𝟕𝟓(𝒏−𝟏) 𝒂𝒏 =𝟕−𝟕(𝒏−𝟏) 𝒂𝒏 =𝟗+𝟔(𝒏 −𝟏) L1.4 Arithmetic Sequences 𝒂𝒏 =𝟓+𝟑(𝒏 − 𝟏) 𝒂𝒏 =−𝟖− 𝟑(𝒏−𝟏) L1.4 Arithmetic Sequences L1.4 Arithmetic Sequences Error Analysis Rami and Sami are given the arithmetic sequence 4,7,10,…. Rami wrote the explicit definition for the sequence. Sami wrote the definition as. Who is correct? Explain. Both are correct because if you simplify Rami’s equation you get Sami’s equation: 2.1 Vertex form of quadratic functions 2.1 Vertex form of quadratic functions a) Graph the function by finding the vertex, the axis of symmetry and the y-intercept. (1,3) Vertex: …………….. To find the y-intercept, replace x by 0 in the equation: x=1 Axis of symmetry: …………. (0,5) y-intercept:…………… b) After graphing the parabola, identify the following: interval increasing:(1,) ……….. () interval decreasing:…………….. Minimum, y=3 Maximum/Minimum:………………….. () Domain: ……………………………….. () Range:………………………………… 2.1 Vertex form of quadratic functions 2.1 Vertex form of quadratic functions 2.1 Vertex form of quadratic functions AFL