Follow the seven step strategy to graph the following rational function. 2x f(x) = x2 - 4 To graph the function, first determine the symmetry of the graph of f. Choose the correct answer below. O origin symmetry neither y-axis symmetry nor origin symmetry y-axis symmetry What is the y-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The y-intercept is. (Type an integer or a simplified fraction.) B. There is no y-intercept. What is/are the x-intercept(s)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The x-intercept(s) is 0. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O B. There is no x-intercept. Find the vertical asymptote(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The equation(s) of the vertical asymptote(s) is/are x = 4,x = - 4 (Type an equation. Use a comma to separate answers as needed.) O B. There is no vertical asymptote. Find the horizontal asymptote(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The equation(s) of the horizontal asymptote(s) is/are y = 0. (Type an equation. Use a comma to separate answers as needed.) O B. There is no horizontal asymptote. Plot points between and beyond each x-intercept and vertical asymptote. Find the value of the function at the given value of x. 5 6 10 5 -7 -6 - 1 1 2x f(x) = x2 - 4 42 9 33 3 (Simplify your answer. Type an integer or a simplified fraction.) Use the information obtained in the previous steps to graph the function between and beyond the vertical asymptotes. Choose the correct graph beld O A. OB. Oc. OD. O D. 10 -10 -10 -10 -10

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.