Subject: Mathematics
Book: Maths Mastery
Rational functions may exhibit asymptotes where they approach but never touch certain lines. Horizontal asymptotes occur if the degrees of numerator and denominator favor a constant limit as x→∞. Vertical asymptotes often appear at values that make the denominator zero (like x=2 if (x–2) is in the denominator). Oblique (slant) asymptotes arise if the polynomial long division yields a linear term with a remainder. Knowing asymptotes helps graph rational functions, interpret large x behavior, and highlight possible domain restrictions. This concept is vital in calculus, ensuring a deeper view of function growth or singularities.
The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?
View QuestionA sum triples in 20 years at simple interest. What is the rate of interest per annum?
View QuestionThe ratio of two numbers is 3:5, and their sum is 64. What are the numbers?
View QuestionIf x:y = 2:3 and z:y = 4:3, what is x:z?
View QuestionIf sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?
View QuestionA sphere has a radius of 7 cm. What is its volume?
View QuestionA rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?
View QuestionA number is increased by 20% and then decreased by 20%. What is the net change?
View QuestionIf sin(A) = 1/2 and A is acute, what is the value of A?
View QuestionIf the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?
View Question