Drawing Other Graphs: Cubic/Reciprocal
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Either paper 3 marksThe table shows some values of \(y = x^3 - 3x + 4\)
Three of the \(y\) values are missing.x -3 -2 -1 0 1 2 3 y -14 6 4 6 (a)Work out the value of \(y\) when \(x = -2\).
(b)Work out the value of \(y\) when \(x = 1\).
(c)Work out the value of \(y\) when \(x = 3\).
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Either paper 3 marks
The graph of \(y = -x^3 + 4x^2 +x - 4\) is drawn on the grid.
On the \(x\)-axis each square is \(1\). On the \(y\)-axis the numbered lines are \(5\) apart, and the fainter lines between them are \(1\) apart.
Use the graph to write down the three solutions of \(-x^3 + 4x^2 +x - 4 = 0\)
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Either paper 2 marks
The graph of \(y = \frac{ 8 }{ x }\) is drawn on the grid. Each square is \(1\).
The graph is in two separate pieces, one in each of two opposite corners.
(a)Use the graph to write down the value of \(y\) when \(x = 2\).
(b)Use the graph to write down the value of \(x\) when \(y = 1\).
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Either paper 3 marks
The graph of \(y = \frac{ 6 }{ x }\) is drawn on the grid.
Both branches bend towards the axes without ever arriving.
(a)Calculate the value of \(y\) when \(x = 2000\).
Give your answer as a decimal.
(b)Explain why the graph never touches the \(x\)-axis.
(c)Explain why the graph never touches the \(y\)-axis.
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Either paper 3 marksThe table gives some values of \(y = \frac{ 38 }{ x }\)
Three of the \(y\) values are missing. Give each of your answers as a decimal.x -16 -4 -2 -1 1 2 4 16 y -2.375 -19 -38 38 19 (a)Work out the value of \(y\) when \(x = -4\).
(b)Work out the value of \(y\) when \(x = 16\).
(c)Work out the value of \(y\) when \(x = 4\).
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Either paper 5 marks
A curve has equation \(y = \frac{ a }{ x }\), where \(a\) is a number.
The curve passes through the point \((2, 6)\).
(a)Calculate the value of \(a\).
(b)Calculate the value of \(y\) when \(x = 6\).
(c)Calculate the value of \(x\) when \(y = -3\).
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Either paper 3 marksA cyclist will travel 24 miles. Draw a graph to show the average speed of the cyclist for the five times taken in the table, 1, 2, 3, 4 and 6 hours. Plot only those five points on the grid. You may use the table to help you.
time taken (hours) 1 2 3 4 6 average speed (mph) 12 4 -
Either paper 4 marksHere is a table of values for \(y = 1 - x^3\) with some of the values missing.
x -2 -1 0 1 2 y 2 0 (a)Complete the table of values. Give the three missing values of \(y\) in the order they appear in the table.
(b)On the grid, draw the graph of \(y = 1 - x^3\) for values of \(x\) from \(-2\) to \(2\).
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Either paper 1 markHere is a graph. Circle the letter of the equation of the graph.
A \(y = 2 - x^3\) B \(y = \frac{ 1 }{ x } + 2\) C \(y = x^2 + 2\) D \(y = x^3 + 2\) -
Either paper 1 mark
\(y = \frac{ 8 }{ x }\)
Which of these values of \(x\) gives the greatest value of \(y\)?
Circle your answer.
\(-78\) \qquad \(0.25\) \qquad \(54\) \qquad \(-0.32\)
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(a) \(2\)
(b) \(2\)
(c) \(22\) - \(x = -1\), \(x = 1\) and \(x = 4\)
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(a) \(4\)
(b) \(8\) -
(a) \(0.003\)
(b) Because y is only 0 when the numerator is 0, and it never is — dividing a fixed number by x always leaves something, however large x gets.
(c) Because a point on the y-axis has x = 0, and you cannot divide by 0, so there is no value of y there. -
(a) \(-9.5\)
(b) \(2.375\)
(c) \(9.5\) -
(a) \(12\)
(b) \(2\)
(c) \(-4\) - A smooth curve through \((1, 24)\), \((2, 12)\), \((3, 8)\), \((4, 6)\) and \((6, 4)\), falling as the time increases
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(a) \(9,\ 1,\ -7\)
(b) A smooth curve through \((-2, 9)\), \((-1, 2)\), \((0, 1)\), \((1, 0)\) and \((2, -7)\)(b) - C: \(y = x^2 + 2\)
- \(0.25\)
Takes a couple of seconds the first time a sheet is made.