Question

Plot the graph f on the graphf(x)=|1/2x-2|

Answer 1

Given : f(x) = | 1/2x -2 |

• We will determine the domain, range and x ;y intercept then plot the graph

1. The domain is given by :

`\begin{gathered} \text{Domain = }x<0\text{ = (-}\infty\text{ },\text{ 0) } \\ \text{ x >0 = ( 0 },\infty)\text{ } \\ \text{ =(-}\infty;0)\text{ U ( 0 ;}\infty) \end{gathered}`

2. Range is given by :

`\begin{gathered} \text{Range = f(x) }\ge0\text{ } \\ \text{ =}\lbrack0;\infty) \end{gathered}`

3. x - and y -intercept :

`x\text{ - intercept = ( }(1)/(4);\text{ 0) }`

4. asymptote :

`\begin{gathered} \text{vertical : }x\text{ = 0 } \\ \text{horizontal : y = 2 } \end{gathered}`

Now that we have the necessary points to plot the f(x) = | 1/2x -2 | , the graph will look as follows :