Which function would result from stretching y = {x) vertically by a factor of 3 and then vertically translating the graph 6 units down? y = 3f(x) – 6 %3D y = 3f(x- 6) y = {3x) – 6 y = (3x - 6)

Q: find the horizontal asymptote(s) for…

A: Simplify the numerator and denominator of the function as follows.

Q: Consider the following. 1 y = 3 – 3x2 + 8x + 1 Find the relative maxima, relative minima, and points…

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Q: The area of the largest rectangle that can be drawn with one side along the x-axis and two vertices…

A: The diagram below shows the rectangle as mentioned in the problem, The rectangle is symmetric about…

Q: neath the graph of f(x) = 7x³ about the y-axis ov

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Q: Sketch the graph of the function

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Q: Given U = VXY; and Px=10 , Py-20, income=100; what is the value of MRSxy at the optimization point?…

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Q: maximum revenue for the revenue function  R(x) = 372x − 0.7x2.  (Round your answer to the nearest…

A: Please refer to the image below

Q: Sx + 1, if { x20} L-2x + 2, if { x < 0} 6)Graph f(x) =

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Q: 1. Find the range of values of x for which y = x3 + 5x2 - 8x + 1 is increasing.

A: We have to find the range value of x

Q: Find the number of units x that produces a maximum revenue R in the given equation. R = 108x2/3 −…

A: R=108x2/3-6x

Q: Given the function y = x2 + 10x + 21, what is the least possible value of y? %3D

A:

Q: Consider choosing x and y to maximise -x-3y, while 1 3y In(3x) + In 3 3 cannot fall below 1.4. What…

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Q: How can the graph of f(x) = -(x -1 ) 2 +6 be obtained from the graph of y = x 2?

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Q: Find the point on the graph of the function that is closest to the given point. f(x) = Vx - 6, (15,…

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Q: Find the point on the graph of the function x = √10y that is closest to the point (0, 4)

A: The given function and point are x=10y and (0, 4) respectively. The graph of the function x=10y is:…

Q: 3. Graph the function. - 2r+ 8 if x<4 (x) = 1 %3D

A: Here we have to graph the given function  f(x)=-2x+8 if x≤412x if x&gt;4

Q: How does the graph of f(x) = (+2)4 + 6 compare to the parent function g(x) = x*? X 6|个 + Source C…

A: Given query is to find the transformation applied.

Q: The graph of y =f(x+3)  is obtained from the graphof y = f(x) by shifting_________ 3 units.

A: Given, y =f(x+3)

Q: If Q(x) =  x^3 − 25x + 100 is the cost per item of producing x-items. Is the cost per item…

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Q: Use the graph of f(x) → 3x² to obtain the graph of h(x) =: 2.

A: Given :      f(x) = 3x2       h(x) = 1/3 x2

Q: How can the graph of f(x) = -4|x| be obtained from the graph of y= Ixl?

A:

Q: A housing complex has 100 two-bedroom units. The monthly profit (in dollars) realized from renting…

A:

Q: 4x² + 9x + 1 3x² + 7x + 5 What is the equation of the horizontal asymptote for y= С. A. x= А. D. y=3…

A: Explained below

Q: x2 - 9 f(x) = %3D x2 + 4x + 3

A: Given fx=x2-9x2+4x+3

Q: What values of a and b, with a < b, minimize the value of (x* – 2r?) dr?

A: The given integral is ∫abx4-2x2 dx. Draw the graph of the function y=x4-2x2 as shown below. .

Q: Find the point on the graph of the function y = 4 - x2 that is closest to the point (0,2)

A: Find a point (x, y), closest to the function.

Q: 2. How does the graph of f (x) =- Vx+4 – 3 differ from the graph of y = - VX?

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Q: Find the point on the graph of the function that is closest to the given point. f(x) = Vx - 4, (15,…

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Q: 1. How does the graph of f (x) = vVx – 2 differ from the graph of y = Vx+ 3 ?]

A: The value of sqrt(x-2) is differ from the value of sqrt(x+3).

Q: Find the equation of horizontal asymptote of y=3(0.2^x)+15pi

A:

Q: Suppose f(x)=−x2+10x−6 models the per household smoothie consumption, in quarts, in the town of…

A: Given that : fx=-x2+10x-6. Therefore, take first order derivative : f'x=-2x+10. At f'(x)=0 , we get…

Q: 2 Q5 / Sketch the graph of function y = =+ 3x

A: Given function is y=2x+3x Domain : ℝ-0 where ℝ denotes the set of real numbers  Range : (-∞,…

Q: 2. For what values of x is y = 150x - 2x3 an increasing function?

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Q: Suppose y = 3x + 2. What is fl.y if x increases by 3?

A: Given y = 3x +2, if x increases by 3, then we have to calculate the change in y.

Q: 1. How does the value of h affect the graph of f(x) = (x – h) + k?

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Q: The sales of a product produces revenue R(x) where x represents the amount spent on advertising.…

A: Solution :-

Q: How does the value of a affect the graph of y = ax? Discuss the case for a 1 and for 0 s a s 1.

A: When a &gt;=1  Graph will shrink towards y axis that is value of y increases more rapidly When 0…

Q: Suppose c(x) = x - 24x2 + 10,000x is the cost of manufacturing x items. Find a production level that…

A: We use second derivative test to find out average cost minimum

Q: Explain how to identify the graph of : Ax2 + Cy2 + Dx + Ey + F = 0.

A: If an equation has a square form of the variable  or a square form of the variable  or a square form…

Q: Q4/A. Draw the graph, of the functions determined by the given formula y = V4 -x

A:

Q: The graph of y= f(x-3) is the graph of y= f(x) 4 A. vertically compressed by a factor of 4 and…

A: Given function y=14f(x-3) with parent function y=f(x).

Q: find the maximum revenue for the function R(x)=356-0.9x^2

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Q: The daily profit from the sale of a product is given by P = 32x − 0.2x2 − 200 dollars, where x is…

A: topic - application of derivatives

Q: Consider the following total revenue function for a hammer. R = 36x – 0.01x² %3! (a) The sale of how…

A: Given Data: The total revenue function is: R=36x-0.01x2 (a) At maximum revenue, the derivative of…

Q: Consider the following production function; Q(K,L) = 3K²/³1ª/3 The firm uses 125.000 K and employs…

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Q: Sketch the graph of f(x)=(x+2)³/²+1 stretch vertically by factor of 3.

A: Given: The function is, fx=x+23/2+1

Q: Find the point on the graph of the equation f (x) = x² – 8 that is closest to the point (0, -2)

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Q: Determine the value of t that maximizes the area above the x-axis and below the graph of the…

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Q: The slope of the graph of the function y = 2x at (32,8) is %3D Tuno n mplifGed fraction

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Q: Use the graph of 5 x %3D x² + 4 to approximate the values of x that satisfy y > 1.

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.