New Zealand
Level 7 - NCEA Level 2

# Find the Equation of a Logarithm Function

## Interactive practice questions

Consider the function $F\left(x\right)=2^x$F(x)=2x.

a

Graph the function.

b

Add the line $y=x$y=x to the graph.

c

By reflecting points on the curve $F\left(x\right)=2^x$F(x)=2x over the line $y=x$y=x, draw the inverse of $F\left(x\right)=2^x$F(x)=2x.

d

What sort of graph have you drawn?

A

Reciprocal

B

Logarithmic

C

Exponential

D

A

Reciprocal

B

Logarithmic

C

Exponential

D
e

Hence state the equation of the logarithmic graph drawn.

Easy
Approx 5 minutes

Consider the function $f\left(x\right)=\left(\frac{1}{5}\right)^x$f(x)=(15)x.

Consider the function $f\left(x\right)=e^x$f(x)=ex.

Consider the function $f\left(x\right)=5\times2^x$f(x)=5×2x shown in the graph.

### Outcomes

#### M7-2

Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs

#### 91257

Apply graphical methods in solving problems