If (-3, 1) is in the function f (x), then which of the following points will be in the function f1 (x)? O (-1, –3) O (3,-1) O (-1, 3) O (1,-3) О (3, 1)

Q: (x-4)(x-3) Determine the points of discontinuity for the function f(x): = (x-3)(x+2) a. (3.- 1/3) 5…

A: To determine the points of discontinuity for the function f(x)=(x−3)(x+2)(x−4)(x−3)​ , we need to…

Q: Which of the following is a point on the graph of the function 5 - 3x f(x) = 4. (-5, 5) (2,-1) (1.4)…

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Q: f = {(-9, – 2), (-8, 5), (-6, 1), (- 3, 7), (–1, – 2),(0, – 10)} and g = {(-7,7), (-6, 6), (-5, 5),…

A: Given that, f = {(-9, -2), (-8, 5), (-6, 1), (-3, 7), (-1, -2), (0, -10)} g = {(-7, 7), (-6, 6),…

Q: what is the equation of the following linear unction f(x) through the points (-5, -2 and (7,-3)

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Q: Which of the following relations is not a function? a.{(3,3), (2,3),(0,4),(1,4)} b. {(3,3), (2,3),…

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Q: Given the function f(x)= { (1,8), (2,16), (3,24), ( 4,32)}, Find the inverse of f-1(x) = {       }

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Q: A bucket has a leak that started 6 hours ago. At time 0, when the bucket just emptied, a tap was…

A: Which option represents  the amount of water in the second bucket.

Q: What is the vertex of the following function? f(x) = x² + 4x +3 (-1,4) (-2,-1) (4,3) (-4, 3)

A: Solution : Given that f(x) = x^2 + 4x + 3 For vertex of the given function , f'(x) = 0

Q: Which of the following represent the order pairs for the function f(x) = 3x + 1 if the domain is {…

A: Given  f(x) = 3x +1  Domain of function is {1, 2 ,3 , 4}    We need to find the ordered pairs for…

Q: Find (f + g)(1). f = {(1, -2), (0, -1)} and g = {(5, 0), (1, -3), (2, -4), (-2,4)}

A:

Q: If(5, –2) is in the function f (x), then which of the following points will be in the function f'…

A: Given that (5, -2) is in the function f(x). So, we have f(5) = -2 and hence f-1(-2) = 5. Thus, we…

Q: Use the function f(x) = 5x – 6 to compute and expand and simplify the following. a. f(-) = b. f(-6a)…

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Q: (-∞, -4): -4 Evaluate the function f(x) at your selected x-value: Will f(x) be positive or negative…

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Q: The domain of f (x) = -x + 4 is {0, 1, 2, 3}, what is the range? O {0, 1, 2, 3} O {1, 2, 3, 4} O…

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Q: Select all of the statements that are true for the functi O f(x) is shifted 4 units to the right. If…

A:

Q: Let f(x)= = -2 x²+3x O Only 0 O Only 3 O Only -3 Only 0 and 3 What values of x have to be excluded…

A: given  f(x)=-2x2+3xfor domain  x2+3x≠0

Q: Refer to the functions f and g and evaluate the functions at x =-2. f = {(2, -1), (1, 1), (-4, -6),…

A: (f+g)(-2)=f(-2)+g(-2)  Substitute   f(-2)=-8  ,    g(-2)=-5in the above equation

Q: If (1, a), (b, ), (c, 17) are points on the graph of the function h(t), which points are on the…

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Q: (-5-х-4):(-2-х-9) Let f(x) = (4:x-2)-(5.x+3) Indicate which of the following points x are in the…

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Q: The function f(x) = -X-3)2 - 4, will have a shift of 4 units to the left. O True O False

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Q: If f (x) = x-x, show that 2.

A: Since this is a multiple question, according to the Bartleby answering rule, only first question is…

Q: Find the rule of the function associated with the following table. 1 2 3 y 1 - 3 -7 -11 y = -4x+1 y…

A: We have to find the function y x 0 1 2 3 y 1 -3 -7 -11

Q: The function f(x) has been transformed to y = -2f(-x+3)+1, which has resulted in the mapping of (4,…

A: We have to find correct option using given data. Concept required:

Q: f={(-4,-7), (1,-4), (8,1)} and g={(-7,9), (1,8), (3,7)} find g of f

A: Given query is to find the composite function g of f

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.