Given that (1,-8) is on the graph of f(x), find the corresponding point for the function f(x).

Q: -x+1 0. Use three key points to sketch the graph of the function g(x) = - ) + 3 starting with the…

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Q: Write the function in its final position. f(x)= x³ first moved 2 units downward, then 3 units to the…

A: The objective is to write the function in its final position.

Q: Find f(a), f(a+h), and the difference quotient for the function given below.

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Q: Sketch the graph of Ax) = x' + x – 4x – 4. Find all values of X %3D -

A: The graph is shown below:

Q: Let f(x)=4x-3. Sketch the graph of f and f-1 and find the rule of f 1,

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Q: 1 1-) f(x) = ?+ 2x - 1

A: The graph of the given fuction Drwan in the last step , at first we describe how t

Q: Let the function *) be represented by the following graph: 3. -2 а. Is this function even, odd, or…

A: Here, we need to find weather the given function f(x) is even or odd or neither of these. And, We…

Q: For the function f defined by f(x) = x2 - 4x + 1, find: f(-x)

A: Here given as fx=x2-4x+1

Q: If f (x) =ax³+ bx² , determine a & b so that the graph of f will have a point of inflection at (1,2)

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Q: Draw the graph of any function f (x) that passes through the point (3, 2).

A: Consider the function  f(x)=x-1. Put x=3. f(3)=3-1=2. So the graph of the function passes through…

Q: Use the graphs of functions f and g to answer the problem. (f. f) (-2) (f. f)(-2) = X f(x) y -X

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Q: Give one way to restrict the domain of the function f (x) = X4-2to make the resulting function…

A: Given function is: fx=x4-2fx=x2

Q: For the function g(x) = x2 - 1, select each value of the range if the domain is equal to {-4, 0, 3}.

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Q: what will the point (0,0) be mapped to when graphing the function f(x)=2sin(x-60)-5

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Q: Given that fX) -4X +5 is a one-to-one function. Determine f

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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.