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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
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

Lesson details

Key learning points

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

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.

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.

Making connections is really powerful when learning mathematics. $$2^{(-1)}={1\over{2^{(1)}}}={1\over2}$$ and $$2^{(-2)}={1\over{2^{(2)}}}={1\over4}$$ is utilising pupils' knowledge of indices.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), 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 $$y=({1\over4})^x$$, what is the value of $$y$$ when $$x=0$$?
$$1\over4$$
$$0$$
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: $$1\over25$$
$$-10$$
Q4.
Which statements are true for $${1\over2}^{100}$$?
It is greater than $$1\over2$$
Correct answer: It is less than $$1\over2$$
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 .
An image in a quiz
Correct Answer: 25
Q6.
Which of these could be the equation of this curve?
An image in a quiz
$$y=4^x$$
$$y=-4^x$$
Correct answer: $$y=4^{-x}$$
$$y=-4^{-x}$$

Exit quiz

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6 Questions

Q1.
The general form for an equation is $$y = ab^x$$.
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?
An image in a quiz
$$y=10^x+10$$
$$y=10^{-x}+10$$
$$y=10^{-x}-10$$
Correct answer: $$y=10^x-10$$