Polynomial functions, sine, and cosine functions have no horizontal or vertical asymptotes. Trigonometric functions csc, sec, tan, and cot have vertical asymptotes but no horizontal asymptotes. Exponential functions have horizontal asymptotes but no vertical asymptotes. The slant asymptote is obtained by using the long division of polynomials.

There are two types of translations of functions. Horizontal translations; Vertical translations; Horizontal Translation of Functions: In this translation, the function moves to the left side or right side. This changes a function y = f(x) into the form y = f(x ± k), where 'k' represents the horizontal translation. Here, if k > 0, then the function moves to the left side by 'k' units. if k ...

In this article, we will be learning about the different aspects of polynomial functions.Polynomial is made up of two words, poly, and nomial. "Poly" means many, and "nomial" means the term, and hence when they are combined, we can say that polynomials are "algebraic expressions with many terms".Let’s go ahead and start with the definition of polynomial functions and their types.

Limits of Functions and Continuity. Limits of the function and continuity of the function are closely related to each other. Functions can be continuous or discontinuous. For a function to be continuous, if there are small changes in the input of the function then must be small changes in the output. In elementary calculus, the condition f(X) →λ as x → a means that the number f(x) can be ...

The exponential function has no vertical asymptote as the function is continuously increasing/decreasing. But it has a horizontal asymptote. The equation of horizontal asymptote of an exponential funtion f(x) = ab x + c is always y = c. i.e., it is nothing but "y = constant being added to the exponent part of the function". In the above two graphs (of f(x) = 2 x and g(x) = (1/2) x), we can ...

Quadratic functions are used in different fields of engineering and science to obtain values of different parameters. Graphically, they are represented by a parabola. Depending on the coefficient of the highest degree, the direction of the curve is decided. The word "Quadratic" is derived from the word "Quad" which means square. In other words, a quadratic function is a “polynomial function ...