Question

if ( g(x)=0.5^{(x + 1)}+2 ), which statement is true?
oa. the horizontal asymptote of ( f(x) ) is ( y = 1 ), and the horizontal asymptote of ( g(x) ) is ( y = 2 ).

Explanation:

Step1: Recall the horizontal asymptote of an exponential function

For an exponential function of the form \(y = a\cdot b^{x - h}+k\), the horizontal asymptote is \(y = k\).

Step2: Determine the horizontal asymptote of \(f(x)\) from the graph

Looking at the graph of \(f(x)\), as \(x\to\infty\), \(y\to1\). So the horizontal asymptote of \(f(x)\) is \(y = 1\).

Step3: Determine the horizontal asymptote of \(g(x)\)

Given \(g(x)=0.5^{(x + 1)}+2\), comparing with the form \(y=a\cdot b^{x - h}+k\), here \(k = 2\). So the horizontal asymptote of \(g(x)\) is \(y = 2\).

Answer:

A. The horizontal asymptote of \(f(x)\) is \(y = 1\), and the horizontal asymptote of \(g(x)\) is \(y = 2\).