Key features of a reciprocal graph | Maths | Quizalize & Oak National Academy

Starter quiz

The ______ of $\frac{1}{9}$ is 9.

'reciprocal' ✓
What is the value of $y$ when $x=3$ in the equation $y=15x$ ? ______

'45' ✓
What is the value of $y$ when $x=3$ in the equation $y={15\over{x}}$ ? ______

'5' ✓
What is the value of $y$ when $x={1\over{2}}$ in the equation $y=12x$ ?

24

12

6 ✓

3
What is the value of $y$ when $x={1\over{2}}$ in the equation $y={12\over{x}}$ ?

6

12

24 ✓

48
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

-24 ✓

Exit quiz

Select the equations that can be plotted to give a reciprocal graph.

$y=2+x$

$y=\frac{2}{x}$ ✓

$y=x^2$

$y=\frac{1}{2+x}$ ✓

$y=2x$
__________ is a line that a curve approaches but never touches.

An asymptote ✓

An axis

An intersection

An intercept

A reciprocal
Which of these statements is true for the graph of $y=\frac{4}{x}+2$

The $x$ -axis is an asymptote

The $y$ -axis is an asymptote ✓

The curve intersects the $x$ -axis ✓

The curve intersects the $y$ -axis
Match each of curve to the equation of its horizontal asymptote

$y=\frac{2}{x}$

⇔

$x$ -axis ✓

$y=\frac{3}{x}+2$

⇔

$y=2$ ✓

$y=\frac{2}{x}+3$

⇔

$y=3$ ✓

$y=\frac{3}{x}-2$

⇔

$y=-2$ ✓

$y=-\frac{2}{x}-3$

⇔

$y=-3$ ✓
The graph of $y = \frac{1}{x-4}$ has a vertical asymptote at $x=$ ______

'4' ✓
Which of these equations could be the equation of this curve?

$y=\frac{3}{x}-2$

$y=\frac{1}{x-2}+3$

$y=\frac{2}{x}-3$

$y=\frac{6}{x}-3$ ✓

$y=\frac{6}{x}+3$

Worksheet

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Lesson Details

Key learning points

A reciprocal graph has a distinct shape.
A reciprocal graph has two asymptotes.
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.