For the given function f (x) = -0.5x² + 2x + 2.5 %3D a) Find the vertex (h, k) b) Find the y intercept c) Find the x intercepts d) Based on the above information graph f (x) e) Determine the range of ƒ (x)

Q: s) find y"= f"(x), given x+y =16 in simplest form.

A:

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A: As the line is parallel, slope of them will be equal. Slope of f(x)=x33+5x22+6x-17 will be :…

Q: Given the function y=3√x. Find d2y.

A: Given

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A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: The horizontal asymptote of x + 5 f (x) = x2 is the line with equation O a y = 1 b y = 0 C X = 1 d.…

A: Given a function f(x)=x+5x2 To find the horizontal asymptote of f(x)

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A: Differentiate the given function and equate to -5 and find coordinate points.

Q: Given a function f(x,y,z) = 2x2 In (6y + 3z). Find the range of the function.

A:

Q: Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per…

A:

Q: + The Range of y [2x + 1] is Z. TO FO

A:

Q: Given k E R, the function f(x, y) = kx² .2 %3D [A) a minimum point, if k = 0 (B) a maximum point, if…

A: Given,  fx,y=kx2+k-1y2+12xy Using second-order partial derivative, check for maxima and minima.

Q: The Range of y = [2x + 1] is Z, T O F

A:

Q: For the graph of the linear function f(x) = mx + b, m is the  _____ and b is the _______ .

A: For the graph of the linear function fx=mx+b, m is the  _____ and b is the _____.

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 10 T, and the line perpendicular…

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Q: The range of the function f(x, y) = 1 3+Vx+y is equal to:

A:

Q: 8. For the graph of the linear function H(z) = -4z + 3, the slope is %3D and the y-intercept is

A: Consider the given equation as Hz=-4z+3

Q: Find domain and range F(x,y)= Vx-1

A: Since you have asked multiple questions in a single request, as per policy, only the first question…

Q: Find the point P on the graph of the function y = yx closest to the point (4,0 The x coordinate of P…

A: Given that, graph of function  y=x   We have to find Point P on y which is closest to (4,0)

Q: The slope of the curve y =x' + 3x² – 4x+5 at (1,5) is O a. 0 O b. 2 O c. 5 O d. 4

A:

Q: Given x = π, y = −1.Find a direct variation model that relates y and x.

A: Given: x=π ,y=-1

Q: Given that f(−2)=−8f(−2)=−8 and f′(−2)=−7f′(−2)=−7, find an equation for the tangent line to the…

A: Given : f(-2) = -8, f'(-2) = -7   To find the equation of the tangent line to the graph of y= f(x)…

Q: Q2: Find all the local maxima, tocal minima, and saddle points of the function f(x, y) = 12xy – 4x*…

A: using derivative

Q: For the function y = f(x) = x² – 2x, x x ≥ 1, find (ƒ-¹) '(3) = df-1 dy y=3

A: We have to find the f-1'(3).

Q: Suppose C is the graph of y = f(x) for a < x < b. Compute x dy + y dx in terms of f.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral.

A:

Q: The Range of y = [2x + 1] is Z, TO F

A: As given function is Greatest Integer Function and we Know that greatest integer function is…

Q: ​Aki's Bicycle Design has determined that when x hundred bicycles are​ built, the average cost per…

A: The average cost per cycle cx=0.1x2-1.2x+3.939 To minimize the cost, let us find the derivative of…

Q: solve for y in terms of t or x, as appropriate.

A: given: lny=-t+5 we have to solve for y in terms of t or x, as appropriate

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A:

Q: The area of the region enclosed by the x axis, the curve y=f(x)>0  for all x ∈ R and the lines x=b2…

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Q: On weekends and holidays, an emergency plumbing repair service charges $60 for the first 30 minute…

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A: We will solve the following

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Q: Suppose (P. 0) is the point on the graph of. y=Vx closest to (1, 0) - What is the value of p + Q? 3…

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Q: When a bus pass from Albuquerque to Los Alamos is priced at p dollars, a bus company takes in a…

A: (a)

Q: 3 f(x) = x2, with 0 < x < 1

A:

Q: . Find all the local maxima, local minima and saddle points of the function below. f(x, y) = 2x³ +…

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Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y…

A: In the given figure, find ∫010g(x)dx ∫1030g(x)dx ∫035g(x)dx We know that definite integral of a…

Q: For what value(s) of x does the graph of f(x) = 8x³ – 84x² + 288x – 48 %3D have a horizontal…

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Q: The Range (Ry) of y = v9 – x² is : - a. [0.] b. (0,3) C. [0,3] d. (0,9)

A: Given that y=√(9-x^2) To find The domain of y.

Q: Given f(x) = x³ – 6x² + 9x – 1 A. Determine the maximum and minimum points. B. Determine the…

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Q: Find a formula for the slope m of the graph of f at the point (x, f(x)). Then use it to find the…

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Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y…

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Q: 18 Find | f(x) dx for each graph of y = f(x). (a) 20- (b) AY 20-

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Q: The function, f, is given by the formula f (x) = x² + kx, where k is a positive constant. The…

A: given function is                                         f(x)=x2+kx point with abscissa…

Q: Find the value of k so that the value of (2y - 1) dy is 10.

A:

Q: Aki's Bicycle Designs gas determined that when x hundred bicycles are built, the average cost per…

A: Consider the given average cost per bicycle is  Cx=0.5x2-0.5x+7.024 where C(x) is in hundreds of…

Q: Aki's Bicycle Designs has determined that when x hundred bicycles are built , the average cost per…

A: Consider the provided cost function.

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.