-
Rational Functions Comprehensive II
Problem 273: For the rational function find the domain, horizontal asymptote, vertical asymptote, holes, -intercept, and -intercept. Solution: (a) To find the domain, we need to find when the denominator is zero. Thus the domain is (b) Since the degree of the polynomial in the denominator is bigger than…
-
Rational Functions Comprehensive
Problem 272: For the rational function find the domain, horizontal asymptote, vertical asymptote, holes, -intercept, and -intercept. Solution: (a) To find the domain, we need to find when the denominator is zero. Thus the domain is (b) Since the degree of the polynomial in the denominator and the denominator…
-
Intercepts of Rational Functions II
Problem 271: For the function Find the – and – intercepts. Solution: To find the intercept, we let . That is, the -intercept is . To find the intercept, we let . Therefore, the -intercepts are and .
-
Intercepts of Rational Functions
Problem 270: For the function Find the – and – intercepts. Solution: To find the intercept, we let . That is, the -intercept is . To find the intercept, we let . Therefore, the -intercept is .
-
Vertical Asymptotes II
Problem 269: Let What is/are the vertical asymptote(s) of ? Solution: The vertical asymptotes of a rational function are given by the values of that makes the denominator zero. Note that since we can simplify the term, is not considered a vertical asymptote. That is, This means that we have two…
-
Vertical Asymptotes
Problem 268: Let What is/are the vertical asymptote(s) of ? Solution: The vertical asymptotes of a rational function are given by the values of that makes the denominator zero. That is, This means that we have two vertical asymptotes which are given by the lines and .
-
Domain of a Rational Function III
Problem 267: State the domain of the function in interval notation! Solution: Finding the domain of a rational expression required us to find the value of that would make the denominator zero. Thus This means that our rational function is defined for all values of except for or $x = -8….
-
Domain of a Rational Function II
Problem 265: State the domain of the function in interval notation. Solution: Finding the domain of a rational expression required us to find the value of that would make the denominator zero. Thus This means that our rational function is defined for all values of except for . Therefore, the domain…
-
Domain of Rational Functions
Problem 265: State the domain of the function in interval notation. Solution: Finding the domain of a rational expression required us to find the value of that would make the denominator zero. Thus This means that our rational function is defined for all values of except for . Therefore, the domain…
-
Fundamental Theorem of Algebra
Problem 264: Give an expression for with leading coefficient 4, of degree 3, and having roots . Solution: Using the Fundamental Theorem of Algebra, we can set up a polynomial with the given roots. That is, Thus the expression for is given by
One Problem at a Time
