The function g is related to one of the parent functions described in an earlier section. g(x) = x2 – 4 (a) Identify the parent function f. f(x) = (b) Describe the sequence of transformations from f to g. (Select all that apply.) O vertical shrink O horizontal shift of 4 units to the left O reflection in the x-axis O vertical shift of 4 units upward O vertical shift of 4 units downward (c) Sketch the graph of g. y y 2d 2아 10 10 X -20 -10 10 20 - 20 -10 10 20 -10 -10 -20아 -20아 y y 2아 10 10 - 20 - 10 10 20 - 20 -10 10 20 -10 -20t (d) Use function notation to write g in terms of f. g(x) = f(

Q: What transformations have occurred to function f(x) if the resulting function is now -2f(x+3)+4

A: Given that the resulting function is -2f(x+3) +4.Here the function f(x) to -2f(x+3) +4 tranformation…

Q: EXAMPLE 6 Composing Functions Given f(x) = x + 2x and g(x) = x – 4, find a. f(g(6)) b. g(f(-3)) c.…

A: Given fx=x2+2x  ;  gx=x-4

Q: 1. Functions Transformation: Write an function for the blue graph (0,0) (1-1) An (3,-2) Bn…

A: The given parent function The transformed function If h<0 then function f(x) shifts h units…

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: f(x)=2(x-4)² +2 Parent: Transformations:

A: Given that, fx=2x-42+2 Write the parent function and their transformations. Parent function is…

Q: 5. To obtain f¹(x) = -x +3+5, the domain of f(x) must be: A. x≤5 B. X25 C. x≤-3 D. x≥-3

A: Given: f-1x=-x+3+5.

Q: 1. Give the dual of each of the following linear programs: (a) maximize 5x₁ +8₂ +3 + 2x4 subject to…

A: Linear programming problem Advance maths

Q: When finding the inverse of a relation, 1st you replace f(x) with y, 2nd switch the x's and y's.…

A: Finding the inverse of a relation: Let's say the relation given by the function f(x)= x+a Where 'a'…

Q: Summary, given some function, f(x), describe the transformation(s) associated with.. a) 2f(x-9)+4 b)…

A:

Q: Use the graphs of f and g to evaluate the functions. y y = f(x) 4 4 y = g(.r) 3 3 2 1 2 (a) (f o…

A:

Q: g(x) = 1/2 |x − 2| − 5   (a) Identify the parent function f. f(x) = (b) Describe the sequence of…

A: Parent function:    The parent function is the basic equation where the function is free from any…

Q: 16.a) lf f(x) = xº, describe the transformations that must be applied to obtain the transformed…

A: Given function isWe can see the domain and range are whole real number.The transformed function…

Q: 3 x – 5. 5 Find the inverse of the function f(x) - f- (x) = - 1 Draw the functions f and f 5- -5 -4…

A: See the details solution in below

Q: 2x + 4 Let f be the one-to-one function given below. f(x) %3D 5z + 6 (a) Find the inverse function…

A:

Q: If the domain of the function y = f(x) equals (-1,5] U [8, 10], what is the domain of the new…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.