F(x) = 2(2/3)^x +3

Question

Domain, y int, range, asymptote.

Answer 1

Domain is all real number since it is an exponential function.

Let x=0 for y intercept. So yint=5.

Since 2(2/3)^x is always greater then zero for any real number x. The range can be defined as y>3 for all x.

It follows that the asymtote is hozontal at y=3 from the previous information about the range.

Answer 2

A graph of (2/3)^x will show the domain and range of a function. Asymptote is the line when the graph approaches infinity.

When x is a real number approaching negative infinity, g(x)=(2/3)^x will approach infinity, and when x approaches positive infinity, g(x)=(2/3)^x will approach 0.

F(X) = 2(2/3)^x+3 can be transformed from g(x) shifting g(x) by 3 in Y direction and stretch by 2.

The graphing can be done using the link below to visualize the range and domain, asymptote line.

https://www.desmos.com/calculator

The domain is (-∞ , +∞) and the range is from (3,+∞). it has a horizontal asymptote at y=3.