a) f(-x)=2⁻ˣ, which is a reflection of f(x) in the y axis.
g(x)=0.5×2⁻ˣ+2=2⁻ˣ⁻¹+2. (Transformation of f(x) to g(x) is reflection of f(x) in the y axis, followed by a horizontal shift left of one unit, then a vertical shift of two units.)
b) To find the y intercept we need g(0)=2.5.
As x>0 gets larger 2⁻ˣ⁻¹ gets smaller so as x→∞, g(x)→2, so g(x)=2 is the asymptote (the line y=2, in other words).
As x<0 gets more negative and x→-∞, g(x)→∞.
c)
d) domain is (-∞,∞). That is the range of x. g(x) is in (2,∞), the range of g(x).