6. Indices, Exponentials and Logs

6.01 Index laws

6.02 Fractional indices

6.03 Scientific notation

6.04 Characteristics of exponential functions

6.05 Graphs and transformations of exponential functions

6.06 Exponential models

6.07 Exponential equations

6.08 Logarithms and indices

6.09 Solving equations with logarithms

Year 11

6.05 Graphs and transformations of exponential functions

Interactive practice questions

Which of the following exponential functions are increasing functions?

Select the two options that apply.

$y=\left(\frac{3}{5}\right)^x$y=(35)x

A

$y=9\times3^x$y=9×3x

B

$y=3\times\left(0.5\right)^x$y=3×(0.5)x

C

$y=0.2\times2^x$y=0.2×2x

D

Easy

1min

Which of the following graphs of exponential functions rises most steeply?

Easy

< 1min

Consider the graphs of the two exponential functions $P$P and $Q$Q.

Easy

1min

Outcomes

1.2.1.4

examine transformations of the graphs of 𝑓(𝑥), including dilations and reflections, and the graphs of 𝑦=𝑎f(𝑥) and 𝑦=𝑓(𝑏x), translations, and the graphs of 𝑦=𝑓(𝑥+𝑐) and 𝑦=𝑓(𝑥)+𝑑; 𝑎,𝑏,𝑐,𝑑 ∈ R

2.1.1.1

recognise and determine the qualitative features of the graph of 𝑦=𝑎^𝑥 (a>0), including asymptotes, and of its translations (𝑦=𝑎^𝑥+𝑏 and 𝑦=𝑎^(𝑥+𝑐))

2.1.1.2

recognise and determine the features of the graphs of 𝑦=𝑏.𝑎^𝑥 and 𝑦=𝑎^(𝑘x) (𝑘≠0)

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