Functions: Questions and Solutions
QUESTION 1
Given: h(x) = −2
1.1 Determine the equation of the asymptotes of h. (2)
1.2 Determine the coordinates of the intercepts of h with the x and y axes. (6)
1.3 Determine the equations of the axes of symmetry of h. (2)
1.4 Sketch the graph of h, clearly showing the asymptotes and ALL intercepts
with the axes. (4)
[14]
QUESTION 2
Refer to the figure. The graphs of f(x)= -2x2 – 4x + 30 and g(x) = 2x + 10 are
drawn (not to scale).
A and B are the x-intercepts and C is the y-intercept of f(x). G is the turning
point of f(x).
A is the x-intercept and D is the y-intercept of g(x). Use the sketch to answer
the questions.
2.1 Determine the coordinates of A, B, C and D. (5)
2.2 Write down the values of x, which f(x) > 0. (2)
2.3 Determine the coordinates of E, one of the points of intersection of f(x) and
g(x). (4)
, 2.4 Determine the equation of the axis of symmetry of f(x). (2)
2.5 Determine the length of GH if GH is parallel to the y-axis. (5)
2.6 If JL=60 units, determine the length of OK. (5)
[23]
QUESTION 3
On a particular day, the depth of water, y metres, at the entrance at tidal
harbour, x hours after midday, is given by the formula:
y = - x2 + 3x + 4 for 0 ≤ x ≤ 4
3.1 Complete the table. (2)
x (hours after 12:00) 0 1 1,5 2 3 4
y (depth in metres) 6 4
3.2 Draw a graph of y against x. (4)
3.3 What is the depth of water at the harbour entrance at midday? (1)
3.4 Determine when during the afternoon the entrance is dry? (1)
3.5 Determine the maximum depth of water at the entrance and when during the
afternoon this occurs. (2)
3.6 A large ferry requires at least 6m of water for it to be able to enter the
harbour. Determine between which times of the afternoon the ferry can safely
enter the harbour. (2)
[12]
SOLUTION 1
1.1 x = -4 ; y = -2
1.2 x-intercept: y = 0
⸫0= −2
0 = 1 – 2 (x + 4)
0 = 1 – 2x – 8
QUESTION 1
Given: h(x) = −2
1.1 Determine the equation of the asymptotes of h. (2)
1.2 Determine the coordinates of the intercepts of h with the x and y axes. (6)
1.3 Determine the equations of the axes of symmetry of h. (2)
1.4 Sketch the graph of h, clearly showing the asymptotes and ALL intercepts
with the axes. (4)
[14]
QUESTION 2
Refer to the figure. The graphs of f(x)= -2x2 – 4x + 30 and g(x) = 2x + 10 are
drawn (not to scale).
A and B are the x-intercepts and C is the y-intercept of f(x). G is the turning
point of f(x).
A is the x-intercept and D is the y-intercept of g(x). Use the sketch to answer
the questions.
2.1 Determine the coordinates of A, B, C and D. (5)
2.2 Write down the values of x, which f(x) > 0. (2)
2.3 Determine the coordinates of E, one of the points of intersection of f(x) and
g(x). (4)
, 2.4 Determine the equation of the axis of symmetry of f(x). (2)
2.5 Determine the length of GH if GH is parallel to the y-axis. (5)
2.6 If JL=60 units, determine the length of OK. (5)
[23]
QUESTION 3
On a particular day, the depth of water, y metres, at the entrance at tidal
harbour, x hours after midday, is given by the formula:
y = - x2 + 3x + 4 for 0 ≤ x ≤ 4
3.1 Complete the table. (2)
x (hours after 12:00) 0 1 1,5 2 3 4
y (depth in metres) 6 4
3.2 Draw a graph of y against x. (4)
3.3 What is the depth of water at the harbour entrance at midday? (1)
3.4 Determine when during the afternoon the entrance is dry? (1)
3.5 Determine the maximum depth of water at the entrance and when during the
afternoon this occurs. (2)
3.6 A large ferry requires at least 6m of water for it to be able to enter the
harbour. Determine between which times of the afternoon the ferry can safely
enter the harbour. (2)
[12]
SOLUTION 1
1.1 x = -4 ; y = -2
1.2 x-intercept: y = 0
⸫0= −2
0 = 1 – 2 (x + 4)
0 = 1 – 2x – 8
