If we were asked to write the transformations y =(x- 2)´ and y =(x+2)´ in terms of the original function f(x) = x² , we could say that y = (x – 2)' = f(x– 2) and y =(x+2)' = f(x+ 2) Summary of Horizontal Shifts If the argument x of a function f is replaced by x-h, h> 0, the graph of the new function y = f(x- h) is the graph of f_ If the argument x of a function fis replaced by x+h, h>0, the graph of the new function h units y = f(x+h) is the graph of f_ h units.

Q: a) A train's path can be modelled by the equation 2 y=-3x+4 What is the closest distance between the…

A: (a) y=-23x+4let the parametric point on the train's path is t,-23t+4 distance between house…

Q: Show that f(x) = (3x - 2) / (5x - 3) , is its own inverse ?

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Q: What can you conclude about the inverses of functions whose graphs are lines parallel to the line y…

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Q: State the transformations of the following function: f(x)= -/4 – 3x +

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Q: For function f(x)=x2 , vertex is the lowest point of this function, which its coordinate is (0, 0).…

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Q: Suppose the functions g and f are defined as follows. h(x) = -5+ 4x2 g (x) = 4 – 9x (ə) Find (4)…

A: Given that, h(x)=-5+4x2 and g(x)=4-9x. Part (a) The value of hg(x) is same as hg(x)=h(x)g(x)…

Q: Differentiate the following functions: a) y = (-5x-7)³ b) y = 7-2x² 2x+1

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Q: coming year. Total profit from planting xj acres at farm j is expressed by the function P(x,, X2,…

A: profit = 235x1 + 540x2 + 252x3 - 525000 we are given that x1 = 300 x2 = 600 x3 = 450

Q: Describe the translation in f(x)= 2*² +5 as it relates to the parent function f(x)=2^

A: Given,          The translation in fx=2x-2+5 as it relates to the parent function fx=2x.

Q: Which of the following functions has a graph with a vertex that is a translation 5 units…

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Q: Graph the pair of functions and identify the transformation of f(x) that produces g(x). S(x) =lx|-2,…

A: To identify: The transformation of fx that produces gx. Given: The functions are fx=x-2 and gx=-x+2.…

Q: Show whether the function y=x² is considered as even or odd function

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Q: If I reverse a function’s components, will this new relation be a function?

A: Suppose a function f(x)=3x+5 with the input of x and gives the result y.

Q: Describe all of the transformations occurring as the parent function f(x)=x² is g(x) = -1 (3(x+4))³²…

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Q: If (2,7) is on the graph of f(x), write the ordered pair that will be on the graph after the…

A: To find ordered pair that will be on graph after the transformation done.

Q: Find the inverse of the function f(x) = 2x +3 / x - 4

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Q: Suppose the coordinate (2, -4) is on the function k(x). If h(x) = k(x + 10) + 5, when k (x) is…

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