Download functions and graphs practice

St Andrew’s Academy
Mathematics Department
Higher Mathematics
E&F 1.3 (Functions and
Graphs)
ASSESSMENT PREPARATION
FUNCTIONS AND GRAPHS PRACTICE
EXPRESSIONS AND FORMULAE 1.3
PRACTICE A
1. The graph of the cubic function y  f (x) is shown in the diagram.
y
On a separate diagram sketch the graphs of:
(a)
y   f (x) .
(b)
y  f ( x  4) . (2)
(2)
3
o
(8,0)
1
x
2. The graphs with equations y  2 x and y  a x are shown in the Diagram.
If the graph with equation y  a x passes through the point (2,9) as shown, find the
value of a.
(1)
y
y  ax
.
10
8
6
.
4
2
-1
(2,4)
.
o
(2,9)
1
2
3 x
3. The graph of the function y  6 x and its inverse function are shown in the diagram.
Write down the equation of the inverse function.
y
(1)
y  6x
(0,1)
o
(1,0)
x
4. Two functions f and g are given by f ( x)  x 2  1 and g ( x)  3x  1 .
Obtain an expression for f  g (x)  .
5.
(1)
A curve with equation y  a cos bx  c 0  x  π has a single maximum value
π

at 0,6  and a single minimum value at  , 2  .
2

(a) Write down the values of a, b and c.
(2, #2.1)
(b) Sketch the curve given by the equation in part (a).
(1)
PRACTICE B
1. The graph of the cubic function y  f ( x) is shown in the diagram.
On a separate diagram sketch the graphs of:
(a)
y   f (x) .
(b)
y  f ( x  4) . (2)
y
(2)
(0,5)
o
-4
2
x
2. The graphs with equations y  3 x and y  a x are shown in the Diagram.
If the graph with equation y  a x passes through the point (1,6) as shown, find the
value of a.
(1)
y
10
.
8
6
(1,6)
.
(2,9)
y  3x
4
2
-1
.
o
1
2
3 x
3. The graph of the function y  7 x and its inverse function are shown in the diagram.
Write down the equation of the inverse function.
(1)
y
(0,1)
o
(1,0)
x
4. Two functions f and g are given by f ( x)  2 x 2 and g ( x)  x  1 .
Obtain an expression for f  g (x)  .
(1)
5.
A curve with equation y  a cos bx  c 0  x  π has a single maximum value
π

at 0,5 and a single minimum value at  , 2  .
2

(a) Write down the values of a, b and c.
(2, #2.1)
(b) Sketch the curve given by the equation in part (a).
(1)
PRACTICE C
1. The graph of the cubic function y  f ( x ) is shown in the diagram.
On a separate diagram sketch the graphs of:
(a)
y   f ( x)  2 . (2)
(b)
y  f ( x  3) .
(-3,4)
(2)
1
o
-5
1
5
x
(3,-3)
2. The graphs with equations y  5 x and y  a x are shown in the Diagram.
If the graph with equation y  a x passes through the point (1,5) as shown, find the
value of a.
(1)
y
10
y  5x
8
6
(1,5)
4
2
-1
.
o
.
.
1
(1,2)
2
3 x
3. The graph of the function y  3 x and its inverse function are shown in the diagram.
Write down the equation of the inverse function.
(1)
y  3x
(0,1)
o
4.
(1,0)
x
Two functions f and g are given by f ( x)  x 2  x and g ( x)  3 x  1 .
Obtain an expression for f  g ( x)  .
(1)
5.
A curve with equation y  a cos bx  c 0  x  π has a single maximum value
π

at 0,10 and a single minimum value at  , 2  .
2

(a) Write down the values of a, b and c.
(2, #2.1)
(b) Sketch the curve given by the equation in part (a).
(1)