algebra
posted by amy
determine the domain, range and horizontal asymptote Please show all your work
f(x) =  (3/4)^x  1
Help!

Reiny
domain : any real value for x
range : y > 1
horizontal asymtote: y = 1
domain and range, just look at a sketch of the graph
last part:
intuitively, as x > ∞+ , value of (3/4)^x > 0
( e.g. (3/4)^100 = 3.2 x 10^13 , pretty close to zero)
as x  > ∞
we get (3/4)^x
= (4/3)^ +x > ∞
so look at x > +∞
f(x) > 0  1 = 1
so y = 1 is the horizontal asymtote
Respond to this Question
Similar Questions

AlgebraI'm still stuck
The onetoone function f is defined by f(x)=(4x1)/(x+7). Find f^1, the inverse of f. Then, give the domain and range of f^1 using interval notation. f^1(x)= Domain (f^1)= Range (f^1)= Any help is greatly appreciated. Algebra … 
Math  Graphing Logarithms function
Graph the function below. Determine the domain, range, and vertical asymptote. Please show all of your work. f(x) = log2(x4) 
Math  Graphing a function
Graph the function below. Determine the domain, range, and horizontal asymptote. Please show all of your work. Submit your graph to the Dropbox. f(x) = (3/2)^(4x) 
pre calculus
graph the function below. Determine the domain, range and horizontal asymptote. f(x) = (3/4)^x  1 
Functions, domain,range etc
Determine the domain,range and horizontal asymptote of f(x)=(3/2)^(4x). Graph the function 
math
graph the function below. Determine the domain, range, and horizontal asymptote. show work f(x)=(7/5)^(x3) 
college alg
use the transformations to identify the graph of the function. then determine its domain, range, and horizontal asymptote. f(x)=4+3^X/3 please show work 
math help please
Consider the function g(x)=x/x7. a) Determine an equation for the vertical asymptote. b) State the domain. c) Determine an equation for the horizontal asymptote. d) State the range. e) Sketch the function. ( i will do it) f) Summarize … 
PreCalculus
State the Vertical Asymptote, Horizontal Asymptote, domain, range, x intercept and y intercept for the following Function. y= (5x)/(x+3) I already know that the Vertical asymptote is 3, so that means the domain is everything except … 
math
find the domain, range, y and xintercept, vertical asymptote, maximum, minimum, onetoone, and horizontal asymptote of: a. f(x)=x^26x+5 b. f(x)=x^26x+5 on domain [1,6]