Question

Plot two points on the graph of the function, and also draw the asymptote.

Answer 1

Write out the function given.

`f(x)=1+\log _2x`

To plot two point in the function, let obtain the point in from the function.

`\begin{gathered} \text{let x=4,} \\ f(x)=1+\log _24 \\ f(x)=1+\log _22^2=1+2\log _22 \\ f(x)=1+2=3 \\ \end{gathered}`

Then, the first point is

`(4,3)`

Similarly, let x=2

`\begin{gathered} \text{if x=2} \\ f(x)=1+\log _22=1+1=2 \\ \text{Then} \\ (2,2) \end{gathered}`

Then the point is

`(2,2)`

The two point to use are

`(4,3)\text{ and (2,2)}`

The point are (2,2) and (4,3)

Then the vertical asymptotes is obtain by equating the logatithm expression to zero

Hence

`x=0`

Vertical asymptotes is x=0

Hence

The image of the graph is given below