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Graphs & Functions Strategies Higher Maths Click to start.

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Presentation on theme: "Graphs & Functions Strategies Higher Maths Click to start."— Presentation transcript:

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2 Graphs & Functions Strategies Higher Maths Click to start

3 Graphs & Functions Higher Graphs & Functons The following questions are on Non-calculator questions will be indicated Click to continue You will need a pencil, paper, ruler and rubber.

4 Hint Quit Previous Next The diagram shows the graph of a function f. f has a minimum turning point at (0, -3) and a point of inflexion at (-4, 2). a) sketch the graph of y = f(-x). b) On the same diagram, sketch the graph of y = 2f(-x) Graphs & Functions Higher a) Reflect across the y axis b) Now scale by 2 in the y direction

5 Hint Quit Previous Next Graphs & Functions Higher The diagram shows a sketch of part of the graph of a trigonometric function whose equation is of the form Determine the values of a, b and c a is the amplitude: a = 4 b is the number of waves in 2  b = 2 c is where the wave is centred vertically c = 1 2a 1 in  2 in 2  1

6 Hint Quit Previous Next Graphs & Functions Higher Functions and are defined on suitable domains. a)Find an expression for h(x) where h(x) = f(g(x)). b)Write down any restrictions on the domain of h. a) b)

7 Hint Quit Previous Next Graphs & Functions Higher a) Express in the form b) On the same diagram sketch i)the graph of ii)the graph of c) Find the range of values of x for which is positive a) b) c) Solve: 10 - f(x) is positive for -1 < x < 5

8 Hint Quit Previous Next Graphs & Functions Higher The graph of a function f intersects the x-axis at (–a, 0) and (e, 0) as shown. There is a point of inflexion at (0, b) and a maximum turning point at (c, d). Sketch the graph of the derived function m is + m is - f(x)

9 Hint Quit Previous Next Graphs & Functions Higher Functions f and g are defined on suitable domains by and a)Find expressions for: i) ii) b)Solve a) b)

10 Hint Quit Previous Next Graphs & Functions Higher The diagram shows the graphs of two quadratic functions Both graphs have a minimum turning point at (3, 2). Sketch the graph of and on the same diagram sketch the graph of y=g(x) y=f(x)

11 Hint Quit Previous Next Graphs & Functions Higher Functions are defined on a suitable set of real numbers. a) Find expressions for i) ii) b) i)Show that ii)Find a similar expression for and hence solve the equation a) b) Now use exact values Repeat for ii) equation reduces to

12 Hint Quit Previous Next Graphs & Functions Higher A sketch of the graph of y = f(x) where is shown. The graph has a maximum at A and a minimum at B(3, 0) a) Find the co-ordinates of the turning point at A. b) Hence, sketch the graph of Indicate the co-ordinates of the turning points. There is no need to calculate the co-ordinates of the points of intersection with the axes. c) Write down the range of values of k for which g(x) = k has 3 real roots. a) Differentiate for SP, f(x) = 0 when x = 1t.p. at A is: b) Graph is moved 2 units to the left, and 4 units up t.p.’s are: c) For 3 real roots, line y = k has to cut graph at 3 points from the graph, k  4

13 Hint Quit Previous Next Graphs & Functions Higher a) Find b) If find in its simplest form. a) b)

14 Hint Quit Previous Next Graphs & Functions Higher Part of the graph of is shown in the diagram. On separate diagrams sketch the graph of a)b) Indicate on each graph the images of O, A, B, C, and D. a) b) graph moves to the left 1 unit graph is reflected in the x axis graph is then scaled 2 units in the y direction

15 Hint Quit Previous Next Graphs & Functions Higher Functions f and g are defined on the set of real numbers by a) Find formulae for i) ii) b) The function h is defined by Show that and sketch the graph of h. c) Find the area enclosed between this graph and the x-axis. a) b) c) Graph cuts x axis at 0 and 1Now evaluate Area

16 Hint Quit Previous Next Graphs & Functions Higher The functions f and g are defined on a suitable domain by a) Find an expression for b) Factorise a) Difference of 2 squares Simplify b)

17 You have completed all 13 questions in this section Back to start Quit Previous Graphs & Functions Higher

18 30°45°60° sin cos tan1 Table of exact values Previous Graphs & Functions Higher


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