Question

Which graph represents f(x)=log2 x+1 ?

Answer 1

The very first graph represents the graph of `f`.

Explanation:

I assume you meant `f(x)=log_2 x +1`

First of all, we see that this function is concave. Basically, any line segment that connects two points on the graph will be below the graph itself. This already eliminates the two right options.

When we want to graph a function, finding its roots is most useful. The roots are solutions of the equation

`f(x)=0`

`:. log_2 x +1 =0`
`:. log_2 x = -1=> x=2^(-1)=1/2`

As such, the graph intersects the x-axis at `1"/"2`.

On the first option, we see that

`f(1/2) = 0`

Which is exactly what we needed. However, let's not jump to conclusions already. At the point `2`, the output is also `2`:

`f(color(red)2)=2`

`log_2 color(red)2 + 1 =2`

`1+1=2 -> " True"`

In the lower graph, we see that the function is `0` at `x=2`. We have already proven this is false.

Therefore, the first graph represents the function `log_2x+1`.