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Year 10
Higher

Key features of a reciprocal graph

I can identify the key features of a reciprocal graph.

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New
New
Year 10
Higher

Key features of a reciprocal graph

I can identify the key features of a reciprocal graph.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. A reciprocal graph has a distinct shape.
  2. A reciprocal graph has two asymptotes.
  3. Reciprocal graphs of the form y = k/x have the axes as their asymptotes.

Common misconception

All reciprocal graphs appear only in two quadrants and have both axes as asymptotes.

Show pupils the graphs of the $$y={1\over{x}}$$, then $$y={1\over{x}}+1$$, then $$y={1\over{x+1}}$$ and get them to compare which forms have which axes as asymptotes.

Keywords

  • Asymptote - An asymptote is a line that a curve approaches but never touches.

Making connections is really important when learning mathematics. Linking the fact that $$y={1\over{x}}+1$$ has an $$x$$-intercept because the equation $${1\over{x}}+1=0$$ has a solution empowers students. Challenge pupils to think 'Can the graph have a $$y$$-intercept?".
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Video

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Starter quiz

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6 Questions

Q1.
The of $$\frac{1}{9}$$ is 9.
Correct Answer: reciprocal
Q2.
What is the value of $$y$$ when $$x=3$$ in the equation $$y=15x$$?
Correct Answer: 45, y=45
Q3.
What is the value of $$y$$ when $$x=3$$ in the equation $$y={15\over{x}}$$?
Correct Answer: 5, y=5
Q4.
What is the value of $$y$$ when $$x={1\over{2}}$$ in the equation $$y=12x$$?
24
12
Correct answer: 6
3
Q5.
What is the value of $$y$$ when $$x={1\over{2}}$$ in the equation $$y={12\over{x}}$$?
6
12
Correct answer: 24
48
Q6.
What is the value of $$y$$ when $$x=-{1\over{2}}$$ in the equation $$y={12\over{x}}$$? A calculator might be useful to check your calculation here.
24
6
-6
Correct answer: -24

Exit quiz

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6 Questions

Q1.
Select the equations that can be plotted to give a reciprocal graph.
$$y=2+x$$
Correct answer: $$y=\frac{2}{x}$$
$$y=x^2$$
Correct answer: $$y=\frac{1}{2+x}$$
$$y=2x$$
Q2.
__________ is a line that a curve approaches but never touches.
Correct answer: An asymptote
An axis
An intersection
An intercept
A reciprocal
Q3.
Which of these statements is true for the graph of $$y=\frac{4}{x}+2$$
The $$x$$-axis is an asymptote
Correct answer: The $$y$$-axis is an asymptote
Correct answer: The curve intersects the $$x$$-axis
The curve intersects the $$y$$-axis
Q4.
Match each of curve to the equation of its horizontal asymptote
Correct Answer:$$y=\frac{2}{x}$$,$$x$$-axis

$$x$$-axis

Correct Answer:$$y=\frac{3}{x}+2$$,$$y=2$$

$$y=2$$

Correct Answer:$$y=\frac{2}{x}+3$$,$$y=3$$

$$y=3$$

Correct Answer:$$y=\frac{3}{x}-2$$,$$y=-2$$

$$y=-2$$

Correct Answer:$$y=-\frac{2}{x}-3$$,$$y=-3$$

$$y=-3$$

Q5.
The graph of $$y = \frac{1}{x-4}$$ has a vertical asymptote at $$x=$$
Correct Answer: 4
Q6.
Which of these equations could be the equation of this curve?
An image in a quiz
$$y=\frac{3}{x}-2$$
$$y=\frac{1}{x-2}+3$$
$$y=\frac{2}{x}-3$$
Correct answer: $$y=\frac{6}{x}-3$$
$$y=\frac{6}{x}+3$$