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

a) b) Graphs & Functions Higher 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) a) Reflect across the y axis b) Now scale by 2 in the y direction Hint Previous Quit Quit Next

2a a = 4 b = 2 c = 1 1 a is the amplitude: 1 in  2 in 2  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 2a 1 a = 4 1 in  2 in 2  a is the amplitude: b = 2 b is the number of waves in 2 c = 1 c is where the wave is centred vertically Hint Previous Quit Quit Next

Functions and are defined on suitable domains. 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) Hint Previous Quit Quit Next

10 - f(x) is positive for -1 < x < 5 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 b) a) c) Solve: Hint 10 - f(x) is positive for -1 < x < 5 Previous Quit Quit Next

f(x) 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 + m is - Hint f(x) Previous Quit Quit Next

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

y=f(x) y=g(x) 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=f(x) y=g(x) Hint Previous Quit Quit Next

a) b) 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) Hint equation reduces to Previous Quit Quit Next

a) b) c) from the graph, k  4 Graphs & Functions Higher Differentiate 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 = 1 t.p. at A is: b) Graph is moved 2 units to the left, and 4 units up t.p.’s are: Hint c) For 3 real roots, line y = k has to cut graph at 3 points from the graph, k  4 Previous Quit Quit Next

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

graph moves to the left 1 unit 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) graph moves to the left 1 unit b) graph is reflected in the x axis graph is then scaled 2 units in the y direction Hint Previous Quit Quit Next

a) b) c) 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 1 Now evaluate Hint Area Previous Quit Quit Next

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

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

30° 45° 60° sin cos tan 1 Table of exact values Graphs & Functions Higher Table of exact values 30° 45° 60° sin cos tan 1 Previous