Answer to Question #178530 in Calculus for sasai

Question

(x^2-3x-4)/(x-4)Factor the numerator of this function. What do you notice about the numerator and denominator of the function, Simplify H(x) and write the new function below as G(x).

 What significant graphical feature is produced when a function like H(x) can be simplified to G(x) ?

 : Graph the function H(x), and clearly state its domain and its range, taking note of the fact that H(x) is not the same as G(x). 

Answer 1

We have given the function,

$H(x) = \dfrac{(x^2-3x-4)}{(x-4)}$

The numerator of this function can be Factorised as $(x+1)(x-4)$

Then G(x) = $(x+1)$

The domain of the function $H(x)$ is $x\in R : x \not =4$

The range of this function $H(x)$ is $y\isin R: y\not=5$