# Use transformations to graph the function determine its domain range and horizontal asymptote

Use transformations to graph the function. Then determine its domain, range, and horizontal asymptote g(x) 2 + 2x + 1 Use the graphing tool to graph the function Click to enlarge graph (For any answer boxes shown with the grapher, type an exact answer) What is the domain of g(x)-2+2*1 Type your answer in interval notation) What is the range of g(x) = 2 + 2x + 1 ? Jan 22, 2015 · Next graph the original function using transformation (Shift up one unit). The graph of passes through , and . Graph: Graph the functions and . Draw the line segment for transformation line . Observe the graph, the domain of function over the interval . The range interval is . The horizontal asymptote of function is the line . Solution:

the graph of y 3 x down one unit. Shift the graph of y 3 x down one unit. 5.1.15 and 18 Use the graph of and transforms to sketch the exponential functions. Determine the domain and range. Also, determine the y-intercept and find the equation of the horizontal asymptote. 3) How do we estimate the value of an exponential funciton using a graph? 4) How do we graph a logarithmic function? 5) What is the relationship between an exponential and a logarithmic function? 6) How do we find the domain and range of a logarithmic function? Standard Form of Exponential Functions: = ᤙ 1. Graph the functions: a. =2ᤙ b. Step 1. Determine the Domain and Range. The domain of a function f(x) is the set of all input values (x-values) for the function. The range of a function f(x) is the set of all output values (y-values) for the function. Methods for finding the domain and range vary from problem to problem. Here is a good review. Step 2. Find the y-Intercept A vertical asymptote represents a value at which a rational function is undefined, so that value is not in the domain of the function. A reciprocal function cannot have values in its domain that cause the denominator to equal zero. In general, to find the domain of a rational function, we need to determine which inputs would cause division by zero.

Jul 18, 2011 · Graph the following function using transformations. Find the vertical and horizontal asymptotes. State the domain and range. Please show work. _____. This link will get you question for blank. h … read more the graph of y 3 x down one unit. Shift the graph of y 3 x down one unit. 5.1.15 and 18 Use the graph of and transforms to sketch the exponential functions. Determine the domain and range. Also, determine the y-intercept and find the equation of the horizontal asymptote. We will use a given Rational Function as an Example to graph showing the Vertical and Horizontal Asymptotes, and also the Hole in the Graph of that Function, if they exist. Begin with the graph of y = e^x. Use transformations to graph the function below. Then determine its domain, range, and horizontal asymptote. f(x) = - 11 - e^-x Use the graphing tool to graph the function.

b) Determine the equation of the horizontal asymptote. (*divide each term by x and simplify*) c) Determine the x-and y-intercepts. d) State the domain and range. e) Sketch a graph of the function and label all important points. f) Complete a table to summarize the intervals of increase and decrease. That is, the function might approach the asymptote as the independent variable gets very large, but it might also cross the asymptote at a small value of x, like x = 0. This crossing does not mean the asymptote doesn't exist. Practice Problem: Graph the function and find its asymptotes. You need not determine the functions for those asymptotes. As we mentioned in the beginning of the section, transformations of logarithmic functions behave similar to those of other parent functions. We can shift, stretch, compress, and reflect the parent function [latex]y={\mathrm{log}}_{b}\left(x\right)[/latex] without loss of shape.

Jun 24, 2013 · A function maps elements of its Domain to elements of its Range. Its Range is a sub-set of its Codomain. For example the function has a Domain that consists of the set of all Real Numbers, and a Range of all Real Numbers greater than or equal to zero. f(x) maps the Element 7 (of the Domain) to the element 49 (of the Range, or of the Codomain).