Question

Graph the function g(x)=(1/2)^x . Which features are correctly stated

A. x-intercept: none
B. y-intercept: (0,1)
C. Asymptote: y = 0
D. as x->oo, f(x)-> oo
E. as x -> -oo, f(x) -> 0

Answer 1

Based on the graph of this function
`g(x)=((1)/(2) )^x`, the features that are correctly stated include;

A. x-intercept: none

B. y-intercept: (0, 1)

C. Asymptote: y = 0

E. as x → ∞, g(x) → 0.

In Mathematics and Geometry, the domain of any logarithmic function is only defined from (x > 0) to infinity (+∞). Thus, its graph moves to the right on the vertical axis and it increases to infinity (+∞) as the value of x increases.

An asymptote is a line which the graph of a given function approaches but would never touch.

Based on the graph of this exponential function, we can logically deduce the following key features;

Vertical asymptote of g(x): none.

Horizontal asymptote of g(x): y = 0.

x-intercept of g(x) = none

y-intercept of g(x) = (0, 1)

In conclusion, the end behavior of this exponential function is that as x approached positive infinity (+∞), g(x) approaches zero (0);

as x → ∞, g(x) → 0.