The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1

Drawing reciprocal graphs

Maths

Checking and securing understanding of drawing quadratic graphs

Key features of a quadratic graph

Drawing cubic graphs

Key features of a cubic graph

Key features of a reciprocal graph

Drawing exponential graphs

Key features of an exponential graph

Drawing the graph for the equation of a circle

Advanced problem solving with non-linear graphs

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.

In this unit graphical representations of non-linear graphs are introduced and explored, and their key features identified.

Non-linear graphs

__________ graphs can have the form $$y={k\over{x}}$$

Which coordinate pairs will appear in the graph of $$y={30\over{x}}$$?

Which coordinate pairs will appear in the graph of $$y={45\over{x}}$$ ?

The $$y$$ values should be positive, not negative.

It does not intercept the $$x$$ or $$y$$ axis.

The curves should be in diagonally opposite quadrants.

It is the graph of a reciprocal equation.

Laura say this is not the graph of a reciprocal equation. How can you tell Laura is correct?

Which of these reciprocal graphs will intercept the $$x$$ axis?

Which coordinate pair is the $$x$$ intercept for the graph of $$y={42\over{x}}-6$$ ?

What is the value of $$y$$ when $$x=5$$ in the equation $$y=15x$$? {{}}

What is the value of $$y$$ when $$x=5$$ in the equation $$y={15\over{x}}$$? {{}}

What is the value of $$y$$ when $$x={1\over{2}}$$ in the equation $$y=6x$$?

What is the value of $$y$$ when $$x={1\over{2}}$$ in the equation $$y={6\over{x}}$$?

What is the value of $$y$$ when $$x=-{1\over{2}}$$ in the equation $$y={6\over{x}}$$? A calculator might be useful to check your calculation here.

Drawing reciprocal graphs

Lesson outcome