Practise Graphs of functions. 1 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.
Question 1Easy3 marks
Here are the equations of four graphs, labelled A, B, C and D.
[object Object]
(a) Here is a sketch of a graph. Write down the letter of the equation of this graph.[1]
[object Object]
(b) Here is a sketch of a graph. Write down the letter of the equation of this graph.[1]
[object Object]
(c) Here is a sketch of a graph. Write down the letter of the equation of this graph.[1]
[object Object]
Show the answer and mark scheme
(a)Answer: C (\(y = 2^x\))
B1 for C
Worked solution: The graph matches \(y = 2^x\), equation C.
(b)Answer: B (\(y = 2x + 1\))
B1 for B
Worked solution: The graph matches \(y = 2x + 1\), equation B.
(c)Answer: D (\(y = 4 - x^2\))
B1 for D
Worked solution: The graph matches \(y = 4 - x^2\), equation D.
Question 2Medium4 marks
Here are the equations of six graphs, labelled A, B, C, D, E and F.
[object Object]
(a) Here is a sketch of a graph. Write down the letter of the equation of this graph.[1]
[object Object]
(b) Here is a sketch of a graph. Write down the letter of the equation of this graph.[1]
[object Object]
(c) Here is a sketch of a graph. Write down the letter of the equation of this graph.[1]
[object Object]
(d) Here is a sketch of a graph. Write down the letter of the equation of this graph.[1]
[object Object]
Show the answer and mark scheme
(a)Answer: F (\(y = x^2 - 4\))
B1 for F
Worked solution: The graph matches \(y = x^2 - 4\), equation F.
(b)Answer: B (\(y = x^3 - 4x\))
B1 for B
Worked solution: The graph matches \(y = x^3 - 4x\), equation B.
(c)Answer: E (\(y = 4 - x^2\))
B1 for E
Worked solution: The graph matches \(y = 4 - x^2\), equation E.
(d)Answer: C (\(y = 2^{-x}\))
B1 for C
Worked solution: The graph matches \(y = 2^{-x}\), equation C.
Question 3Hard4 marks
The graph of \(y = x^2 - 4x + 3\) is drawn on the grid.
[object Object]
(a) Use the graph to explain why the equation \(x^2 - 4x + 3 = -2\) has no solutions.[1]
(b) By drawing a suitable straight line on the grid, use the graph to solve \(x^2 - 5x + 4 = 0\).[3]
Show the answer and mark scheme
(a)Answer: The lowest point of the curve is \((2, -1)\), so \(y\) is never −2: the line \(y = -2\) does not meet the curve.
C1 for explaining that the minimum value of \(y\) is −1 (turning point (2, −1)), so the line \(y = -2\) does not cross the curve
Worked solution: The solutions would be where the curve meets the line \(y = -2\). The minimum of the curve is at \((2, -1)\), above \(y = -2\), so they never meet.
(b)Answer: \(x = 1\) and \(x = 4\) (using the line \(y = x - 1\))
M1 for rearranging to \(x^2 - 4x + 3 = x - 1\)
M1 for the line \(y = x - 1\) drawn correctly
A1 for \(x = 1\) and \(x = 4\)
Worked solution: \(x^2 - 5x + 4 = 0\) is the same as \(x^2 - 4x + 3 = x - 1\). Draw \(y = x - 1\): it meets the curve at \((1, 0)\) and \((4, 3)\), so \(x = 1\) or \(x = 4\).