1. Transformation of Functions Momina Khan City of Westminster College

2. Topic Maths (AS Computing) Aims  Investigate transformation of functions Level Level 3 Method  Using the graphing programme follow the activities in the worksheets overleaf Equipment  PC or laptop  Internet Duration 30 minutes

3. To understand how the following transformations (translations and stretches) affect the graph of the curve y = f(x):1) y = f(x) + a 2) y = f(x) + a) 3) y = af(x) 4) y = f(ax) By the use of a graphing program. https://www.desmos.com/calculator Transformation of Functions Learning Objectives

4. 1.y = f(x) + a Use the graphing program to sketch the graph of f(x) = x 2 Then sketch the graph of y = f(x) + 2 and y =f(x) - 2 Sketch the three graphs in the space below, labelling each graph: Try different values for the constant a. What do you notice? Repeat the procedure with a different graph e.g. cubic or reciprocal. Complete the sentence below: f(x) + a Transformation of Functions

5. 2.y = f(x + a) Use the graphing program to sketch the graph of f(x) = x 2 Then sketch the graph of y = f(x + 2) and y = f(x -2) Sketch the three graphs in the space below, labelling each graph: Try different values for the constant a. What do you notice? Repeat the procedure with a different graph e.g. cubic or reciprocal. Complete the sentence below: f(x + a) Transformation of Functions

6. 3.y = af(x) Use the graphing program to sketch the graph of f(x) = x 2 Then sketch the graph of y = 2f(x), y = 10f(x) and y = - f(x) Sketch the three graphs in the space below, labelling each graph: Try different values for the constant a. What do you notice? Repeat the procedure with a different graph e.g. cubic or reciprocal. Complete the sentence below: af(x) Transformation of Functions

7. 4.y = f(ax) Use the graphing program to sketch the graph of y = 9 - x 2 Then sketch the graph of y = f(2x) and y = f(½ x) Sketch the three graphs in the space below, labelling each graph: Try different values for the constant a. What do you notice? Repeat the procedure with a different graph e.g. cubic or reciprocal. Complete the sentence below: f(ax) Transformation of Functions

8. Try the following questions to consolidate your observations. First identify the transformation that has taken place. Work out whether the original x or y coordinates have been affected. 1.The following diagram shows a sketch of the curve with equation y = f(x). The points A(0,2), B(1,0), C(4,4) and D(6,0) lie on the curve Sketch the following graphs and give the coordinates of the points A, B, C and D after each transformation a f(x + 1)b f(x) - 4c f(x + 4) d f(2x)e 3f(x)f f(½x) g ½f(x)h f(- x) 2.The diagram shows the graph of the quadratic function f. The graph meets the x-axis at (1,0) and (3, 0) and the minimum point is (2, - 1). a Find the equation of the graph in the form y = f(x) b On separate axes, sketch the graphs of i y = f(x + 2)ii y = f(2x) c On each graph write in the coordinates of the points at which the graph meets the x-axis and write in the coordinates of the minimum point. Transformation of Functions

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