Hey there could someone please help me with this

Which one of the following is not true of the graph of the function f:R+ -> R, f(x)=log2(x)?
(where 2 is the base of log)

A) It has a vertical asymptote with equation x=0
B) It passes through the point (2,0)
C) The slope of the tangent at any point on the graph is positive
D) It has domain R+
E. It has range R

Thanks

Why not just graph it and see which is not true?

Graph \frac{log(x)}{log(2)}

If x=2, do you get 0 as a solution?

Domain:

Logs are defined for only positive real values.

Hence Domain of log x is R+

log x can have any real values

Hence Range of log x is R

Passes through (2, 0)?

y = log x (base = 2)

When x = 2, y = log 2 = 1

Hence does not pass through (2, 0)

Tangent Slope

y = log2 x = (loge x)/loge 2

dy/dx = 1/(x log 2) (base e)

It is positive for positive values of x

Asymptote

Asymptotes are formally defined using limits.

The line x = a is a vertical asymptote of a function f

Lim f(x) = (+ or -) infinity as x approaches a

In your case find the limit of f(x) when x aproaches 0