2. Let f a function such that f (-2) = 6, f (0) = – 3, ƒ (3) = 0. Give the coordinates of three points on the graph of y = f(x + 4).

Q: Graph the functions

A: The vertical asymptote occurs if the denominator is 0 Since the degree of the denominator is more…

Q: Determine which of the following equations defines y as a function of x. (a) x-y = 16 (b) x-2y = 8

A: x-y2=16 On simplification, we get ⇒y2=x-16⇒y=±x-16 Clearly for each value of x, there are two values…

Q: Determine whether the equation xy - 5y = 1 defines y as a function of x.

A: Here we determine whether the equation xy-5y=1 defined y as a function of x.

Q: Determine whether the equation defines y as a function of x : x + y = 16

A: The given equation is x+y=16.

Q: y 21 12 4 8.

A:

Q: If (4,y) is an ordered pair of the function,then y =

A: We have to find y, if If (4, y) is an ordered pair of the function.

Q: Is the function f(x) = x3 one-to-one?

A: Given: fx=x3 Horizontal line test: If no horizontal line intersects the graph of the function more…

Q: Identify the graph of a function for which f' and f" take on the following sign combinations in…

A: Given query is to find the correct graph.

Q: 6. Indicate verbally how the graph of each function relates to the graph of one of the six basic…

A: Definitions:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.