Question

Which graph represents f(x)=log2x−1 ?

Answer 1

log x would be like the first graph but pass though the point (1,0)

lg ( x - 1) would pass through (2,0)

so its the first graph

Answer 2

Logarithmic expressions can be represented on graphs

The graph that represents $\mathbf{f(x) = log_2x - 1}$ is graph (a)

The function is given as:

$\mathbf{f(x) = log_2x - 1}$

Start by testing the options.

On graph (a), we have the following points

(x,y) =  (4,1) and (2,0)

Substitute the values for in the function

$\mathbf{f(4) = log_2(4) - 1}$

Evaluate log(4)

$\mathbf{f(4) = 2 - 1}$

$\mathbf{f(4) = 1}$

Also, we have:

$\mathbf{f(4) = log_2(2) - 1}$

Evaluate log(2)

$\mathbf{f(4) = 1 - 1}$

$\mathbf{f(4) = 0}$

These two points are true for $\mathbf{f(x) = log_2x - 1}$

Hence, the graph that represents $\mathbf{f(x) = log_2x - 1}$ is graph (a)

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