The general form for an exponential equation is y = ab^x where a is the coefficient, b is the base and x is the exponent.

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

Key features of an exponential graph

Maths

Checking and securing understanding of drawing quadratic graphs

Key features of a quadratic graph

Drawing cubic graphs

Key features of a cubic graph

Drawing reciprocal graphs

Key features of a reciprocal graph

Drawing exponential graphs

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

The general form for an {{ }} equation is $$y = ab^x$$. 

The $$y$$ values decrease rapidly as the $$x$$ values increase.

The $$y$$ values increase rapidly as the $$x$$ values increase.

Select the statements that are true for the graph of $$y = 10^x$$.

The $$x$$-axis an asymptote to both curves.

The $$y$$-axis an asymptote to both curves.

The curves are symmetrical about the $$x$$-axis.

The curves are symmetrical about the $$y$$-axis.

Laura draws the graphs of $$y=5^(-x)$$ and $$y=5^x$$ on the same pair of axes. Which of these statements are correct.

The $$y$$ values decrease as the $$x$$ values increase.

Select the statements that are true for the graph of $$y = 0.5^x$$.

Match each exponential curve to its asymptote.

Which of these could be the equation of this curve?

In the graph of $$y=({1\over4})^x$$, what is the value of $$y$$ when $$x=0$$?

In the graph of $$y=5^x$$, what is the value of $$y$$ when $$x=-2$$?

Which statements are true for $${1\over2}^{100}$$?

Here is a table of values for $$y=5^{-x}$$. The missing value is {{}}.

Key features of an exponential graph

Lesson outcome