Domain And Range Of A Function With Asymptotes

D x x 5 f x f x graph each function.

Domain and range of a function with asymptotes. Oh you were wondering what the relationship is. Subsection 3 6 1 domain intercepts and asymptotes given a function f x text there are several important features that we can determine from that expression before examining its derivatives. Let s understand the domain and range of some special functions through examples.

A vertical asymptote represents a value at which a rational function is undefined so that value is not in the domain of the function. 16 5 x 1 f x 0. Textbook solution for glencoe algebra 2 student edition c2014 1st edition mcgraw hill glencoe chapter sh problem 8 9ep.

You ll need to find the vertical asymptotes if any and then figure out whether you ve got a horizontal or slant asymptote and what it is. The function y a x a geq 0 is defined for all real numbers. Well we know that the domain of a function is the interval of x values where the function exists and the range is the interval of y values where the function exists.

Identify the asymptotes domain and range of each function. The domain of the function take note of values where f does not exist. A reciprocal function cannot have values in its domain that cause the denominator to equal zero.

Hence the domain of the exponential function is the entire real line. The range for this function would be y in mathbb r all real numbers but y neq frac 1 2 due to the horizontal asymptote at y frac 1 2 the questions of domain and range become more interesting when considered in relation to functions defined by graphs or in applications. The horizontal asymptotes is at y k.

If the function is rational look for where the denominator is zero. Use the domain of a rational function to define vertical asymptotes. Domain and range of exponential functions.