Question

In: Advanced Math

For the following exercises, graph the transformation of f(x) = 2x. Give the horizontal asymptote, the domain, and the range. f(x) = 2x − 2

For the following exercises, graph the transformation of f(x) = 2x. Give the horizontal asymptote, the domain, and the range.

f(x) = 2x − 2

Solutions

Expert Solution

Consider the graph of the function;

f(x) = 2x-2

 

The horizontal asymptote of the function is determined as follows:

 

Check horizontal asymptote for x ± ∞;

f(∞) = 2(-∞)-2

       = 0

 

Therefore, the horizontal asymptote is y = 0.

 

Domain of the graph is set of all real numbers, that is (-∞, ∞).

 

Range is set of all real numbers greater than 0.

 

The graph of the function y = 2x-2 is shown below;


Related Solutions

For the following exercises, graph the transformation of f(x) = 2x. Give the horizontal asymptote, the domain, and the range. h(x) = 2x + 3
For the following exercises, graph the transformation of f(x) = 2x. Give the horizontal asymptote, the domain, and the range.h(x) = 2x + 3
For the following exercises, make tables to show the behavior of the function near the vertical asymptote and reflecting the horizontal asymptote. f(x) = 2x/(x + 4)
For the following exercises, make tables to show the behavior of the function near the vertical asymptote and reflecting the horizontal asymptote.f(x) = 2x/(x + 4)
Graph the function f(x) = 3.5(2)x. State the domain and range and give the y-intercept.
Graph the function f(x) = 3.5(2)x. State the domain and range and give the y-intercept.
For the following exercises, make tables to show the behavior of the function near the vertical asymptote and reflecting the horizontal asymptote. f(x) = 1/x -0 2
For the following exercises, make tables to show the behavior of the function near the vertical asymptote and reflecting the horizontal asymptote.f(x) = 1/x -0 2
For the following exercises, each graph is a transformation of y = 2x. Write an equation describing the transformation.
For the following exercises, each graph is a transformation of y = 2x. Write an equation describing the transformation. 
f(x)= (4x)/(x2-4) Domain Vertical Asymtote Horizontal Asymtote slant asymptote
f(x)= (4x)/(x2-4) Domain Vertical Asymtote Horizontal Asymtote slant asymptote
The graph here shows transformations of the graph of f(x) = 2x. What is the equation for the transformation?
The graph here shows transformations of the graph of f(x) = 2x. What is the equation for the transformation?
Find the vertical asymptote (V.A.) and the horizontal asymptote (H.A.) of the function g(x) = 2x/...
Find the vertical asymptote (V.A.) and the horizontal asymptote (H.A.) of the function g(x) = 2x/ x- 5. Justify your answer using limits. a) The equation of the V.A. is ________ and the associated limit is: b) The equation of the H.A. is ________ and the associated limit is:
1) Find the domain and range of the rational function y( x) = x^2-25 / 2x^2...
1) Find the domain and range of the rational function y( x) = x^2-25 / 2x^2 + 13x+15 A) Factor the numerator and denominator B) Determine the point of discontinuity if it exists.
5. Consider the function f(x) = -x^3 + 2x^2 + 2. (a) Find the domain of...
5. Consider the function f(x) = -x^3 + 2x^2 + 2. (a) Find the domain of the function and all its x and y intercepts. (b) Is the function even or odd or neither? (c) Find the critical points, all local extreme values of f, and the intervals on which f is increasing or decreasing. (d) Find the intervals where f is concave up or concave down and all inflection points. (e) Use the information you have found to sketch...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT