The graph f(x)- x² is transformed to create m(x) - f(bx)², where "b" is less than 1 but greater than 0. Which graph best represents the two functions? %3D

Q: The function f(x) = -x2 + 46x - 360 models the daily profit, f(x), in hundreds of dollars, for a…

A: Differentiating with respect to x, we get Again differentiating with respect to x, we get Now

Q: What is the effect on the graph f (x) = |3x -4| when it is replaced by f (x) + 3?

A: For tranformation of  f(x)→f(x)+a if a > 0  graph will shift a units up if a < 0 graph will…

Q: how is the graph g(x)=(x-6)^2-4 related to the graph of f(x)=x^2?

A: In this question transfomation takes place.

Q: Use the graph of f(x) = 2x to obtain the graph of g(x) = 2x - 3.

A: Given

Q: How Is the graph of g (x)=x2+14 related to the graph of f(x)=x2? The graph of g (x)=x²+14Is the…

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Q: Analyze the graph of the function. Зх- 12 H(x) = 16 -x

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Q: Draw the graph of f(x) – (x + 3)?

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Q: The graph of the function f(x) = 3x4 - x3 + 5x2 - 2x - 7 resembles the graph of ________ for large…

A: The graph of the function f(x) = 3x4 - x3 + 5x2 - 2x - 7resembles the graph of ________ for large…

Q: How is the graph of g(x)=(x-3) related to the graph of f(x) = x?

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Q: Find an equation for the graph sketched below -5 4 -3 f(x) =

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Q: s the graph of /(x), which function g(x)-4(x-C)+D hn as its graph?

A: Given query is to find graph of g(x) from f(x).

Q: Which of the following represents the graph of f(x) = 2(x − 3)?

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Q: Suppose that the x intercepts of the graph of y=f(x) are -5 and 3. What are the x intercepts of the…

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Q: -3x – 5 is obtained from the graph of f (x) = |x| + 1.b) Describe how the graph of g (x) = -|x| Зх +…

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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: True or False The graph of f(x) = 2x2 + 3x - 4 opens up.

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Q: The graph of g(x) = ax2 opens downward and is narrower than the graph of f(x) = x2  what is value a?

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Q: Which is the graph of f (x) 2x + 8x ? = -x Which is the graph of h (x) = 2(x + 1)(x´ - 9) - 2(+ +…

A: Given, fx = -x4 -2x3 +8x2  hx = 2x+1x2 -9  we have to choose the graph of fx  and  hx

Q: how do you draw the graph of f ( x ) = 5^(x + 4)

A: We have to graph the given function.

Q: True or False The graph of f(x)=2x2+3x-4 opens up.

A:

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 f(x) = x2 – 7 is horizontally stretched by a factor of 4.5. Write the equation…

A: Here the graph of f(x)=x²-7 is horizontally stretched by a factor of 4.5.  We want to write the…

Q: Compare the graphs of the two functions f(x) = 2* and g(x)/ Determine the equation of (x). 15. g(x)…

A: Given,           The graph of fx and gx are shown below :            fx=2x

Q: Use the function’s equation, f(x) = -x2 + 14x - 106 and not its graph, to find; a. the minimum or…

A: we have been given  f(x) = -x2 + 14x - 106 we have to tell the minimum and maximum value . also we…

Q: 2. How does the value of k affect the graph of f(x) = (x- h) + k?

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Q: Sketch the graph of f(x) = 6**4

A: It is given that                        F(x)=6x+4 Now we want to draw the graph of F(x) So we will…

Q: How does the graph of g(x) = 4x + 5

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Q: Use the function’s equation f(x) = -x2 + 14x - 106, and not its graph,to finda. the minimum or…

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Q: For Exercise, graph the function. x² + 2x + 1 |k(x) =

A: We find the vertical asymptote by setting the denominator equal to 0.  So, x=0 is a vertical…

Q: 7. Use the graph of f(x) → 3x² to obtain the graph of h(x) =x² .2

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Q: Q3, sketch the graph of Hhe function y= x-4x +3

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Q: The axis of symmetry of the graph of f(x)=2(x+9)2-3 has equation...

A: Given,

Q: Explain how the graph of f(x) = mx + b can be used to solve mx + b &gt; 0.

A: f(x)=mx+ b

Q: Given the functions )-x-4 and gx)-x-1, a graph of the combined function y- most likely resembles a)…

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Q: Given the graph below, solve f(x) > g(x) -5 -4 -3/-2 -1 F-1 -2 -3 -4 -5+ of

A: According to the given information, Consider the given graph:

Q: How would the graph of f(x) = ✔x be affected if it were changed to g(x) = -2✔x?

A: Because the 2 was multiplied with f(x), so f(x) will stretch vertically by a factor of 2.  Because…

Q: Draw the graph of f(x)=2-|x|, and use it to find the 2 value of |(2- a1) da. -2 Write your answer as…

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Q: 29. f(x) = -3x² + 5 (0,5)

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Q: The graph of f(x) =x^2 rises or falls to the left? And rises or falls to the right?

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Q: What is the zeros, y-intercept, vertex, and axis of symmetry of f(x)=-2x^2-5x+3.  What does a graph…

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Q: P3, sketch the graph of the function y= x-4x +3

A: Since you have posted multiple questions, so we solve the first question for you, to get the…

Q: Fill in each blank so that the resulting statement is true.

A: Compared with the graph of fx=1x, the graph of gx=1x+2-1 is shifted 2 units ______ and 1 unit _____.

Q: If g(x) = x2 – 4, where does the graph of the g(x) cross the x-axis? Make a sketch of the graph.

A: Given g(x)=x2-4We know that x2 graph is a prabola

Q: how is the graph of g(x)=x³+2 related to the graph of f(x)=x^3

A: The graph of  x3 and x3+2 are related to each other.  Both the graphs work in same sense but graph…

Q: Draw the graph of f(x) = 5+3

A: We make a table of different values of x and y. The function is f(x)=5x+3 x 0 1 -1 ∞ y 125 600…

Q: Use the graph of f(x) = x2 to graph g(x) = (x + 3)2 + 1.

A: fx=x2 The graph is,

Q: Draw the graph of f(x)=(1/6)x+2

A: Given :

Q: Draw the graph of the function y = 3x2 +1

A:

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.