1. Graphs of Exponential Functions 1y 1 2 3 4 5 7 6 8 -1 -2 -3
You need to be familiar with the function 𝑦= 𝑎 𝑥
For example, y = 2x, y = 5x and so on…
Draw the graph of y = 2x 8 4 2 1
1/2
1/4
1/8 y 3 -1 -2 -3 x
Remember:
Any graph of will be the same basic shape
It always passes through (0,1) as anything to the power 0 is equal to 1

2. Logarithms and
growth functions
Graphs

3. Exponential graph: Richter Scale
Key Q: is 8 on the richter scale twice as much as 4 on the richter scale (No – it’s a logarithmic scale / exponential graph)
Why is this a logarithmic scale? – need to investigate further
Nepal 2015
(7.3)

4. Graphs growth and logarithm
KUS objectives
BAT recognize key features of growth graphs and logarithmic graphs
Starter: Imagine plotting a graph of 𝑦= 2 𝑥 with 1 m to one unit on each axis
How far along the x-axis would you go before the graph reached the top of a sheet of paper? If you extend the graph so the x-axis fills the whole width of a sheet of paper, how tall will the paper have to be?
2 𝑥 =21 gives roughly =21 𝑘𝑚
2 𝑥 =30 gives roughly 𝑥=4.9
How far along the x-axis would you have to go so that the graph was tall enough to reach:
to the top of The Shard in London?
to the moon?
to the Andromeda galaxy?
2 𝑥 = for the shard 𝑥=14.9
2 𝑥 =2.5 𝑚𝑒𝑔𝑎𝑙𝑖𝑔ℎ𝑡𝑦𝑒𝑎𝑟𝑠 for Andromeda 𝑥 = 81
Full solutions

5. WB1 Graphs of growth functions All pass through (0,1)
Here are a few more examples of graphs of growth (exponential) functions
They never go below 0
y = 3x
Notice that either side of (0,1), the biggest/smallest values switch
Above (0,1), 𝑦 = 3𝑥 is the biggest, below (0,1), it is the smallest…
y = 2x
y = 1.5x

6. The graph y = (1/2)x is a reflection of y = 2x
WB2 Graphs of Exponential Functions
The graph y = (1/2)x is a reflection of y = 2x
y = 2x
y = (1/2)x
All graphs of the form y = a-x have the blue shape and go through (0, 1)

7. Graphs of Logarithmic Functions Open the Geogebra file
‘exp and inverse’
What will the inverse of an exponential function look like?
Drag point A around to find out

8. They do not exist for 𝑥 < 0
WB3 Graphs of Logarithmic Functions
Here are a examples of logarithm graphs
y = log2x
y = log3x
y = log10x
All pass through (1, 0)
They do not exist for 𝑥 < 0

9. WB4 solving by inspection
Some equations involving indices can be solved by inspection. Try these:
𝑎) 2 𝑥 =16
𝑒) 𝑥 =9
𝑏) 10 𝑥 =0.001
𝑓) 𝑥 =21
𝑐) 5 𝑥 =625
𝑔) 𝑙𝑜𝑔 10 𝑥=0
𝑑) 𝑥 =81
ℎ) 𝑙𝑜𝑔 10 𝑥=3
Check your answers with a calculator
Can you see any connections / patterns?:

10. WB5 investigate
Think about the function 𝑦= 10 𝑥 . Every time we increasex by one, we multiply  𝑦  by  10.
By how much do we multiply  𝑦 when we increase  𝑥 by  0.5 ?
What does the whole number part of the power of ten tell us about the value of y ?
How is this connected with standard form?
Can you find approximate solutions to the following equations:

11. One thing to improve is –
KUS objectives BAT recognize key features of exponential graphs and logarithmic graphs
self-assess
One thing learned is –
One thing to improve is –

12. END