An exponential function with a base of 1/2 has been compressed vertically by a factor of 3/4 and reflected in the y-axis. Its asymptote is t

a) Write an equation of the function

b) Discuss its domain and range

Hello Guest!

a)
\(\color{blue}f(x)=\frac{3}{4}\cdot (\frac{1}{2})^x+t\\ f(0)=\frac{3}{4}+t \)

reflected in y

\(\color{blue}g(x)=\frac{3}{4}\cdot (\frac{1}{2})^{-x}+t\\ f(0)=\frac{3}{4}+t \)

b)

domain f(x) and g(x):  - \(\infty\) < x < \(\infty\) 

range f(x):   t < f(x) < \(\infty\) 

range g(x):   t < g(x) < \(\infty\) 

  !