New Zealand
Level 8 - NCEA Level 3

Linear Functions and Inverses

Interactive practice questions

Consider the function $f\left(x\right)=x+1$f(x)=x+1.

a

Graph the function on the set of axes below:

b

Is the function $f\left(x\right)=x+1$f(x)=x+1 a one-to-one function?

No

A

Yes

B

No

A

Yes

B
c

If a function is one-to-one, an inverse function exists. Find the inverse function $f^{-1}\left(x\right)$f1(x), writing each line of working as an equation:

Easy
Approx 3 minutes

Define $y$y, the inverse of $f\left(x\right)=-4x$f(x)=4x.

Define $y$y, the inverse of $f\left(x\right)=8x-1$f(x)=8x1.

Consider the function $y=3x+8$y=3x+8.

Outcomes

M8-2

Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions