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

Key features of a reciprocal graph

Maths

In this unit, pupils consider other types of graphs. In the future unit, pupils consider different types of sequences such as Fibonacci and oscillating. Their knowledge is consolidated by linking all prior learning together.

In the prior unit, pupils studied the graphical representation of a geometric sequence and linked features of the graph to its equation. In this unit, other types of graphs are introduced and their key features identified.

Non-linear graphs

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

 __________ is a line that a curve approaches but never touches.

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

Match each of curve to the equation of its horizontal asymptote 

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

Which of these equations could be the equation of this curve?

What is the value of $$y$$ when $$x=3$$ in the equation $$y=15x$$? {{}}

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

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

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

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.

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