State whether the following mappings are one-to-one, many-to-one, one-to-many or many-to-many.
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State whether the following mappings are one-to-one, many-to-one, one-to-many or many-to-many.
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The function is defined as
Sketch the graph of , giving the coordinates of any points where the graph intersects the coordinate axes.
The minimum point on the graph of has -coordinate 4.
Find the range of .
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The function is defined as
Work out the range of .
If the domain of is changed to what would be the new range of ?
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The functions and are defined as follows
Find
Solve the equation .
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The function is defined by
Find the inverse of
Find the domain and range for .
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State whether the following mappings are one-to-one, many-to-one, one-to-many or many-to-many.
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The function is defined as
Sketch the graph of giving the coordinates of any points where the graph intercepts the coordinate axes and the coordinates of the turning point.
Write down the range of
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The function is defined as
Work out the range of .
If the domain of is changed to what is the range of ?
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The functions and are defined as follows
Write down the range of .
Find
Solve the equation
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The graph of is shown below.
Use the graph to write down the domain and range of
Given that the point (1, 1) lies on the dotted line, write down the equation of the line.
On the diagram above sketch the graph of
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The function is defined as
Show that can be written in the form
Explain why the inverse of does not exist and suggest an adaption to its domain so the inverse does exist.
The domain of is changed to .
Find an expression for and state its domain and range.
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The functions and are defined as follows
Find
Write down and state its domain and range.
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It is given
Write down the domain of the function .
Sketch the graph of stating the coordinates of any intersections with the coordinate axes and the equations of any asymptotes.
Write down the range of
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The function is defined as
Work out the range of
If the domain of is changed to , what is the range of ?
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The functions and are defined as follows
Write down the range of .
Find
Solve the equation
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The graph of is shown below.
On the diagram above sketch the graph of .
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The functions and are defined as follows
Find
Write down and state its domain and range.
The graphs of and are drawn on the same axes.
Describe the transformation that would map one graph onto the other.
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It is given
Write down the domain and range of the function
Sketch the graph of stating the coordinates of any intersections with the coordinate axes. (You do not need to give the coordinates of any turning points.)
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The function is defined as
Work out the range of
If the domain of is changed to , what is the range of ?
State another domain for that would have the same effect as that in part (b).
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The functions and are defined as follows
Write down the range of
Leaving your answers as single fractions, find
Solve the equation
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The graphs of and (dotted line) are shown in the diagram below. has rotational symmetry about the origin and for , there is a vertical line of symmetry at
Use the graph to write down the domain and range of
On the diagram above sketch the reflection of in the line y = x and explain why this cannot be the graph of
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The function is defined as
Explain why the inverse of does not exist.
Suggest an adaption to the domain of so the following conditions are met:
State the range for your adapted .
The domain of is changed to
Find an expression for and state its domain and range.
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The functions and are defined as follows
Find
Write down and state its domain and range.
The graphs of and are drawn on the same axes.
Describe the transformation that would map one graph onto the other.
Find the coordinates of the point where the graphs of and meet.
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