Explain how the graph of g is obtained from the graph of f. (a)     f(x) =    x,    g(x) = −   x + 9 reflect about the x-axis, then shift up 9 unitsreflect about the y-axis, then shift down 9 units    shift up 9 units, then reflect about the x-axisreflect about the y-axis, then shift up 9 unitsreflect about the x-axis, then shift down 9 units

Q: Explain how the graph of g is obtained from the graph of f. x-5 %D

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Q: Sketch the graph of f.

A: Consider the given information. fx=ex-2 Make the table for the function. x fx=ex-2 -2 e-4 -1…

Q: Q3/ Sketch the graph of f(x) = x+1

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Q: Explain how the graph of g is obtained from the graph of f. (a) f(x) = x3, g(x) = (x - 8)3 shift…

A:

Q: True or False The graph of a function y = f1x2 alwayscrosses the y-axis.

A: Given : Statement : The graph of a function y=f(x) always crosses the y-axis. Determine the given…

Q: Use transformations on the graph of y = f(x) = 8 to graph g(x) = 8 *. ... Use the graphing tool to…

A: Solution: Given data, y= 8x g(X)=8-x

Q: The rate at which snow fell on a cul-de-sac street on a particular day can be modeled by the…

A: You must have idea about standard form of parabola in order to understand the problem.

Q: Use graphical addition to sketch the graph of f+g.

A: Consider the given graph.

Q: Sketch the graph of f′. Explain how you found your answer.

A: we can observe that equation of given curve is like fx=mx;m>0 now we have to find f'x

Q: suppose (-2,1) is a point on the graph of y=f(x). what is a point that will be on the graph of…

A: Topic - functions

Q: How does the graph of f(x) = 2*+2 compare to the graph of g(x) = 2* + 2? The graph of f(x) is a…

A: The graph f(x) is a translation of the parent function h(x) =2x 2 units to the left Given functions…

Q: Find the point of diminishing returns for the function, where R is the revenue (in thousands of…

A: The given function is, R=-14x3+3x2+8 The interval is 0 ≤ x ≤ 8

Q: Find the point of diminishing returns for the function, where R is the revenue (in thousands of…

A: Given that: Rx=-14x3+3x2+8,        0≤x≤8…

Q: Find the point of diminishing returns for the function, where R is the revenue (in thousands of…

A: Solution

Q: How is the graph of f (a)= (x - 4)° transformed from its parent function?

A:

Q: Use a graphing utility to graph f(x) = (x2 - 4x + 3)/(x - 2), and g(x) = (x2 - 5x + 6)/(x - 2). What…

A: Given: f(x)=x2-4x+3x-2 g(x)=x2-5x+3x-2 To find: The graph of f and g and also  differences between…

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

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Q: 4) Graph the function f(x) = x² and g(x) x² + 7

A: Graph.

Q: left, right, upward, downward (a) How is the graph of y = f(x - 2) +1 obtained from the graph of f?…

A: Given (a) y=f(x-2)+1

Q: Explain how the graph of g is obtained from the graph of f. (a) f(x) = Vx, g(x) = -Vx + 9 %3D %3D O…

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Q: Graph F(x) = -(x + 1)(x – 1)^2(x – 2) by doing the following. Plot all the points where the graph…

A:

Q: What's the relationship between (x)^1/2 and (x)^2? Based on their properties and graphs

A: whats the relationship between the given curve

Q: How are the graphs of f(x) = x and g(x) = -f(x) – 1 related?

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Q: %3D Let X be the graph of f(x) = x2/3 given below

A: Follow the steps.

Q: Describe the relationship between the graph of ​f(x)=x2−2x+4 and the graph of y=x2

A: To determine: Ther relation between the graphs of given two functions. Given equations:…

Q: Approximate the value of g"(0.5). Giving a reason for your answer, what does this value say about…

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Q: Explain how you test if the graph of y = f () is ncreasing or decreasing.

A:

Q: Sketch the graph of f′. Explain how you found your answer.

A: Given,

Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

A:

Q: What is the effect on the graph of f(x)= x when g(x)= + 4?

A: when you add +4 in function  e.g f(x)=x g(x)=f(x+4)=x+4

Q: 2. or For the graph of y = f(x) shown below, sketch the graph of y = = √√f(x). State the domain and…

A: A real valued function makes a defined relationship between two subsets of real number line. The…

Q: Explain how the graph of g is obtained from the graph of f. f(x) =x², g(x)=x² +2

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

A:

Q: How can you find the values of x for which f(x)=3 using the graph? what points do you look for?

A: For finding the values of x for which f(x) = 3, we draw the line y = 3 on the same graph as f(x) and…

Q: My graph of f(x) = 3 . 2x shows that the horizontal asymptote for f is x = 3.Determine whether the…

A: Consider the given function as fx=3·2x

Q: How does the graph of f () = a²compare to the graph of g (2) = (x + 2)² – 7? The graph of 9 (æ) is…

A: Shifting of graph

Q: f(x)=x^4+5x, find f'(x). What is the graph?

A: Let the function f(x) is given as  f(x)=x4+5x   To determine: The derivative of the function f(x)…

Q: Identify the vertex of the following.f(x) = (x − 6)2 + 3Use a graphing utility to verify your…

A: f(x) = (x − 6)2 + 3 is in vertex form  We compare it with  f(x)=a(x-h)2+k  So, h=6 and k=3    So,…

Q: What is the end behavior of the graph of f(x) = – 0.5x2 – 3x – 4? A.as x increases, f(x) increases;…

A: The given function is

Q: How can the graph of function fg be obtained from the graphs of functions f and g?

A: To obtain a graph of fg from the graphs of f and g, it is necessary to multiply f and g. Then, we…

Q: 2 Explain how the graph of y = -f(x - 2) compares to the graph of y = f(x).

A: The given function: y=-f(x-2) Parent function: y=f(x)

Q: Explain how the graphs of g and h are obtained from the graph off. f(x) = x², g(x) = (x + 4)°,…

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Q: (a) How is the graph of y = f(x – 3) + 2 obtained from the graph of f? %3D (b) How is the graph of y…

A: Shifting or change in the graph of the function f(x) is done by adding, subtracting, multiplying,…

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: Starting with the graph of f(x) = 9², write the equation of the graph that results when: (a) f(x) is…

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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.