Use the given graphs of f and g to evaluate each expression, or if the expression is undefined, enter UNDEFINED. (a) f(g(2)) (b) g(f(0)) |x (c) (fo g)(0) |x (d) (g o f)(6) UNDEFINED (e) (g o g)(-2) (f) (fo f)(4)

Q: Sketch the graph of f(x) = In |x| and explain how the graph 1 shows that f'(x)

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Q: Give an example of a function whose domain D has three elements and whose range R has two elements.…

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Q: etch a graph of f(x) = 4 -3 -2 -1 5 4 3 2- 1 -1 -2 -3 -4 -5 if x 2 1 2 3

A: Topic:- function

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: 2х + 5 if x 2

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Q: The domain of f is [-4, -1) ∪ (-1, 4].Use the graph to determine whether the statement is true or…

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Q: The graph of f(x)=-x -5x+6 has the point (2, -6) on it. O True O False

A: We can check the answer is true or false as below

Q: Find f.g and f-g. Then, give their domains using interval notation.

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Q: 11. Use the graph of f(x) to graph f-1(x).

A: Here is the solution of the given problem.

Q: If ƒ and g are real-valued functions, how are the domains of ƒ + g, ƒ - g, ƒg, and ƒ/g related to…

A: Consider that f and g to be a real-valued function then the addition, subtraction, product and…

Q: Graph f(x) = 1/2|x + 4 | – 5 and create a table of values f(x) = 1/2|x+4|-5 f(x) 3 2- -6 -5 -4 -3 -2…

A: Given that,f(x)=12x+4-5 x f(x) Points=(x,f(x)) -4 -0.2 A=(-4,-0.2) -1 1 B=(-1,1) 0 0.3333…

Q: Given f(x) = x + 4 and g(x) : x +5 a. State the domain of f(g(x)) in interval notation. Domain: b.…

A: Let's find.

Q: Sketch the graph of f(x) = -3x³-4x² + 6x-2 by following the steps in sketching the graph of a…

A: A graph is said to be concave up at a point if the tangent line to the graph at that point lies…

Q: Sketch a graph that shows f'(x) and f''(x) are always negative

A: answer is in next step

Q: The function f is defined by ƒ (x) = -2x³ – x – 5 and f(-1) = -2. If g(x) = f¯1(x), what is the…

A: Given fx=-2x3-x-5f-1=-2Therefore, f-1-2=-1Differentiate with xf'(x)=-6x2-1f'-1=-7

Q: 2- Correctly identify the end behavior of the graph of f(x). O 1+ 00, f (r) 00; -00, (x) → - 00 O 1…

A: We need to find the end behaviour of the graph shown above.

Q: -6 9. 4- -6-

A: First, from graph we will find values of f(2) and g(2) and then we will find (f+g)(2) as shown below

Q: The domain of f (x) = -x + 4 is {0, 1, 2, 3}, what is the range? O {0, 1, 2, 3} O {1, 2, 3, 4} O…

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Q: escribe the end behavior of the graph of the function  a) f(x)= -4(8)^x -3 as x-->negative…

A: Given function  f(x)=-48x-3

Q: The graph of f(x)=-x-5x+6 has the point (2, -6) on it. O True O Fals

A: Ans: False

Q: Discuss the continuity and sketch the graph. x-2 if x1

A: as per our guidelines we can answer only 1 question do kindly repost the remaining questions…

Q: Suppose that f(3) = 2, f'(3) = 5, and f' (x) > 0 and f"(x) < 0 for all values of x in (-0, 00).…

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Q: list a sequence of transformations in words to convert the graph of f(x)=x2 into the graph og…

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Q: Sketch a graph of: f(x) = 2|x+3|– 1 5+ %3D 4 -5 -4 -3 -2 -1 4 5 -1 -2- -3 -4 -5+ 2. 3. 2.

A: Answer is mentioned below

Q: 1 if x 1 5- 4 -5 -4 -3 -2 -1 2 3 4 5 -2 -3 -4 -5+ Clear All Draw: /

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Q: 4. If the point (3, -5) is on the graph of a one-to-one function f, what point must be on the graph…

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Q: The graph of f is given. State, with reasons, the numbersat which f' is not differentiable.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Suppose the function f has a domain set of all real numbers. Given below is the graph of f(x). f'(x)…

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Q: if the point (2,8) is on the graph of f, then f(2) =

A: The point 2,8 is on the graph of f.

Q: f(X)こ 34ーオー2

A: The given function is fx=3x-x-2To find the point when x=2

Q: 4. If f(x)= and g(x)=determine the domain of g(f(x))?

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Q: an the graph of f(x), determine the domain off-(x). [10,-) [2.-) - f(x)

A: Topic:- function and it's inverse

Q: 9. Given the functionf (x) = |x| + 4, state the domain and range. Domain: [-4, 0) Range: (-0, ∞) O…

A: Given function is  fx=x+4

Q: If f(x) = -√x and g(x) = √-x, then f and g have identical graphs.Determine whether each statement is…

A: If f(x) = -√x and g(x) = √-x, then f and g have identical graphs.Determine whether each statement is…

Q: Let f = {(- 2,1),(1, - 1)} and g = {(-2, - 4),(3,0),(5,6)}. Find f+g and its domain.

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Q: 0. if a 2

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Q: Sketch the graph of f.

A: The given function is fx=x-11-x2. Sketch the graph of the above function as shown below.

Q: Sketch a graph of f(x) = -4 if x 2

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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: 3 if a 2 5- -5 -4 -3 -2 -1 -1 4 -2 -3 -4 -5- Clear All Draw: 3.

A: The sketch of the given function has been provided in next section.

Q: Sketch the graph of f'(x) for f(x) = x³ + x³ . Label at least 3 points on this graph .

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Q: 2A.6A: analyze the effect on the graphs of f(x) = x, when f(x) is replaced by af(x), f(bx), f(x -…

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Q: Sketch a graph that has all the given character f(-1) = 2 and f(2) = 4 interval (-, -1) || (-1, 2) |…

A: Graph passing through the points (-1,2) and (2,4)

Q: 1 if x 2

A: Given the piecewise functionf(x)={1   if x≤-2-x-1  if -2&lt;x≤2-2    if x&gt;2  We need to graph the…

Q: x + 4 if x 1 |

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Q: defined by f(x) = (x-5)^2 - 20 for all real numbers x. What is the range of f ?

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Q: If the point (3,7) is on the graph of f, then f(3) =               .

A: We know that if any point (x, y) is on the graph of any function f then f(x) = y

Q: х — 6 if x 1 | 7

A: GIven:f(x)=-x-6   if x≤-2  -3         if -2&lt;x≤1x-4      if x&gt;1To sketch the above piecewise…

Q: 5. Define the function f(x) = |x| • |x – 3| piecewise without absolute value bars and graph.

A: Use the definition of modeule of a function on each factor and combined them

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.