The graph of y =g(x) is the image of the graph of y = f(x) after a reflection and a stretch. The ordered pair (-2, 5) is on the graph of y = f (x) and (8, 5) is on the graph of y = g(x). 15. The correct relationship between f(x) and g(x) is Og(x) = -4f(x) Oala) -() Og(x) = f 4 Og(x) = f(-4x) Og(2) =7 (2)

Q: Given the function g(x) = 4x° + 12x² – 180x, find the first derivative, g'(x). = (x),6 Notice that…

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Q: Find the absolute maximum value of the function y=xV3x-x² on the interval [0, 3].

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Q: 3. The amount of money ($125 per day) paid to substitutes at LHS depends on how many teachers are…

A: a)  Number of substitutes  =  20*0.8 + 2  =  18     Hence,  Money paid by LHS for substitutes  =…

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: In 2009, the federal income tax T on income of x dollars (up to $82,250) was determined by the…

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Q: 1-x3 , х0 . Sketch the graph.

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Q: 1) Find the minimum value of the curve y = 3x + 2x - 3. Plot the graph for values of x between -2…

A: We have to find the minimum value of the curve y=3x2+2x-3 over the interval -2<x<3.

Q: f(x) = (x +2)²(x – 1) f'(x) = 3x(x+2) f"(x) = 6x +6 %3D

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Q: 1. Use the first derivative test to find the local minimum and maximum points of the graph of f(x) =…

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Q: ) Suppose we shift the graph of f vertically downwards by h units such that the maximum turning…

A: Given, the function f and g are defined by              f(x)=acosk(t-b)and              g(x)=mcsc…

Q: Match the function with its graph. I II y 1 III IV (a) f(x) = x2 ---Select--- (Б) f(x) = x3…

A: use the basic concept of function and  graph we get the match.

Q: 1) Find a function y whose graph passes through the point (1, ) and satisfies x?y' = y.

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Q: Given the function g(x) = 4x° + 6x² – 24x, find the first derivative, g'(x). = (x),6 Notice that…

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Q: O Fend an equalion of the tangont line to the graph-of y-x-4Vx at (1-3). O Find an equalion -of #he…

A: If the slope of a line and any point (x1,y1) on it is known then its equation is given by :…

Q: 1) Find a function y whose graph passes through the point (1, and satisfies x?y' = y.

A: We have to solve

Q: Find values of a and b so that the function f(x) = x + ax +b has a local minimum at the point (7, -…

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Q: Given the function g(x) 6x – 27x2 – 72x, find the first derivative, g'(x). = (x),6 Notice that g'(x)…

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Q: for what value of x does the function  f(x) = 1/3 x3 - 4x attain the absolute minimum in the…

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Q: -) Graph Y = 3*2), show critical points, where graph crosses the “X" & “Y" axes.

A: Making the graph of function we can see that graph cuts y axis and is an asymptote to x axis as…

Q: what is the slope of the curve

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Q: Given the function g(x) = 8x + 96x + 360x, find the first derivative, g'(x). %3D = (x),6 %3D Notice…

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Q: Sketch the graph of y = (x² – 1)² – (2x – 1)². [In your answer, you must include the following: •…

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Q: How can you display the values of a function ƒ(x, y) of two in-dependent variables graphically? How…

A: For a  function ƒ(x, y) of two in-dependent variables. It can be plotted graphed using 3d plotting…

Q: I am stuck on the maximum and minimum values of y and corresponding x.  Will you please assist on…

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Q: Given the function g(x) = 8x³ + 12² – 48x, find the first derivative, g' (x). g'(x) = Notice that…

A: We can solve this as follows:

Q: Find a function y whose graph passes through the point (1, =) and satisfies x2y' = y.

A: NOTE: Refresh your page if you can't see any equations. .

Q: Determine the maximum number of turning points of f. 6. f(x) = (x – 2)2(x + 4)2 7. Identify the end…

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Q: Consider the image attached of the graph of a function y = g(x) on the domain -8 <= x <= 8, which…

A: Label the points on the given graph as shown below.

Q: | 1) Find a function y whose graph passes through the point (1, ) and satisfies x²y' = y.

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Q: Given the function g(x) = 6x³ + 27x² 72x, find the first derivative, g'(x). g'(x) = 0 when x = -4,…

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Q: 2) Sketch the graph of the floor function f(x) = x+31 over the interval [-4,2].

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Q: The graph of f(x) = 2a² + 12z² – 72z + 14 has two horizontal tangents. One occurs at a negative…

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Q: Find the value of x at which the minimum of the function f(x) = x? Occurs.

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Q: Find the value of x at which the absolute minimum occurs (if it exists) for the function f(x) = -x2…

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Q: The slope y-intercept form of a linear relation is represented by y=mx+by=mx+b.  Which equation…

A: Solution: The objective is to find equation shows x isolated correctly for this formula

Q: Parameterize the following curve 9x 9x^2 + 4y^2 = 32y -54x-109

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Q: Can you help with this problem step by step?

A: Given: -

Q: Why does Newton's method fail at all of these points in the graph except for x=5, especially when…

A: Since the graph cut at two point. at x=2, x=6 and graph never touch the  negative x-axis. and…

Q: 1 - X 0 3

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Q: 3.Find the coordinates of the points on the curves y =x3 -3x2-12x+10 with the gradients -2.

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Q: Given the function g(x) = 8x° + 84x² + 288x, find the first derivative, g’(x). = (x),6 Notice that…

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Q: 8. The y-intercept is -4. The function has no x--00, f(x) → -0∞, x-intercepts. As x→ 0, f(x) → -∞…

A: 8.  The y-intercept is -4.   The function has no x-intercepts.  As x→∞, f(x)→-∞ and as x→-∞, f(x)→-∞

Q: On the interval x∈(1,2), the curve y=x^3−6x^2+9x+1 is. decreasing and concave down horizontal…

A: Option A is correct..

Q: A function y = f(x) is decreasing on the interval [0, 5]. What conclusions can you draw about the…

A: A function is increasing, if when x increases, the value of y also increases.          Since the…

Q: y is a linear function of x with slope −4. If y is −3 when x is −1, what is y when x is 8? You do…

A: Linear Function  Y= mX+c  m= slope of function  c = Y intercept

Q: Sketch the graph of y = (x – 3)*(x + 1)³(x - 1) by finding its intercepts and its limits as x → o…

A: topic - functions

Q: On the graph of f(x) = cos x and the interval [-27, 0), for what value of x does f(x) achieve a…

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Q: The line tangent to the graph of g(x) = x³ – 4x +1 at the point (2, 1) is given by the formula L(x)…

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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.