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Year 10

Higher

Key features of an exponential graph

I can identify the key features of an exponential graph.

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New

Year 10

Higher

Key features of an exponential graph

I can identify the key features of an exponential graph.

Download all resources

Share activities with pupils

These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

A exponential graph has a distinct shape.
An exponential graph has one asymptote.
The laws of indices explain where this asymptote is.

Keywords

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

Common misconception

$y = b^{x}$ will reach zero; the curve will touch the $x$ axis eventually.

Get pupils to input large absolute $x$ values to appreciate that no matter how small the $y$ value it is still a fraction greater than zero.

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Making connections is really powerful when learning mathematics.

2^{(- 1)} = 1 o v e r 2^{(1)} = 1 o v e r 2

and

2^{(- 2)} = 1 o v e r 2^{(2)} = 1 o v e r 4

is utilising pupils' knowledge of indices.

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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.

y = 2^{x}

will form __________ graph.

a linear

a quadratic

a reciprocal

Correct answer: an exponential

Q2.

In the graph of

y = (\frac{1}{4})^{x}

, what is the value of

y

when

x = 0

\frac{1}{4}

0

Correct answer:

1

4

Q3.

In the graph of

y = 5^{x}

, what is the value of

y

when

x = - 2

25

- 25

Correct answer:

\frac{1}{25}

- 10

Q4.

Which statements are true for

{\frac{1}{2}}^{100}

It is greater than

\frac{1}{2}

Correct answer: It is less than

\frac{1}{2}

Correct answer: It is very close to 0

It is very close to 1

Q5.

Here is a table of values for

y = 5^{- x}

. The missing value is .

Correct Answer: 25

Q6.

Which of these could be the equation of this curve?

y = 4^{x}

y = - 4^{x}

Correct answer:

y = 4^{- x}

y = - 4^{- x}

Exit quiz

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6 Questions

Q1.

The general form for an equation is

y = a b^{x}

Correct Answer: exponential

Q2.

Select the statements that are true for the graph of

y = 10^{x}

Correct answer: The point (0, 1) lies on the curve.

The point (1, 0) lies on the curve.

Correct answer: The point (1, 10) lies on the curve.

The

y

values decrease rapidly as the

x

values increase.

Correct answer: The

y

values increase rapidly as the

x

values increase.

Q3.

Laura draws the graphs of

y = 5^{(} - x)

and

y = 5^{x}

on the same pair of axes. Which of these statements are correct.

Correct answer: The

x

-axis an asymptote to both curves.

The

y

-axis an asymptote to both curves.

The curves are symmetrical about the

x

-axis.

Correct answer: The curves are symmetrical about the

y

-axis.

Q4.

Select the statements that are true for the graph of

y = {0.5}^{x}

The

y

axis is an asymptote

Correct answer: The

y

values decrease as the

x

values increase.

The point (1, 0) lies on the curve.

Correct answer: The point (0, 1) lies on the curve.

The point (-1, -0.5) lies on the curve.

Q5.

Match each exponential curve to its asymptote.

Correct Answer:

y = 2^{x} - 3

y = - 3

$y = - 3$

Correct Answer:

y = 3^{x} - 2

y = - 2

$y = - 2$

Correct Answer:

y = 2 - 3^{x}

y = 2

$y = 2$

Correct Answer:

y = 2^{x} + 3

y = 3

$y = 3$

Q6.

Which of these could be the equation of this curve?

y = 10^{x} + 10

y = 10^{- x} + 10

y = 10^{- x} - 10

Correct answer:

y = 10^{x} - 10

Key features of an exponential graph

Key features of an exponential graph

These resources will be removed by end of Summer Term 2025.

Slide deck

Lesson details

Key learning points

Keywords

Common misconception

How to plan a lesson using our resources

Licence

Lesson video

Worksheet

Starter quiz

6 Questions

Exit quiz

6 Questions