Higher Ink Exercise
E & F - Graphs and Functions
Calculators should only be used when necessary
1. The diagram below shows the graph of the function y = f(x).
C
A
B
5
a)
On separate axes, sketch the graphs of:
i. y = f(x) + 2
ii. y = f(x + 4)
iii. y = -f(x + 1)
iv. y = -2 - f(x)
v. y = f-1(x)
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b)
If you had the equation of the function f(x), explain how you could find:
i. Point A
ii. Point B
iii. Point C
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2. Three functions, g(x), h(x) and j(x) are defined by:
g(x) = 3x + 2
h(x) = 5 - x2
j(x) = √x
a)
b)
Find an expression for:
i. h(g(x))
ii. g(h(x))
iii. h(h(x))
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For the expression j(g(x)), show that a suitable domain for x would be x ≥ - ⅔
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3. Part of the graph of f(x) = 2x is shown below.
y=2x
(1,2)
a) Sketch the graph of the inverse of this function. Label where this graph cuts
the x -axis
b) Sketch the graph of f(x) = 3f(x).
c) Sketch the graph of f(x) = 2f(x) + 1.
d) Sketch the graph of f(x) = 2-x – 8. Label where this graph cuts both axes.
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4. The diagram below shows part of the graph of y = log2(x).
a)
b)
c)
Find the values of a and b.
State the function of the inverse of this graph.
Sketch the graph of y = log2(x + 1) – 3.
5. Write down the equation of this graph.
6. Sketch the graph of y = 3sin (x - 2π) for 0≤x≤2π
3
Clearly show the maximum and minimum values and where it cuts both axes.
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