Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

      Key features of an exponential graph

      Lesson details

      Learning outcome

      I can identify the key features of an exponential graph.

      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.

      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.

      Teacher tip

      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.

      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).

      Lesson video

      Loading...

      Prior knowledge starter quiz

      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: $$y=4^{-x}$$
      $$y=-4^{-x}$$

      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: $$y=10^x-10$$

      To help you plan your 10 maths lesson on: Key features of an exponential graph, download all teaching resources for free and adapt to suit your pupils' needs...