Let f and g be functions, If the graph of g is obtained from the graph of f by translating the graph of f two units to the left, which of the following gives the relationship between f(x) and g(x)?

Q: Determine (algebraically) whether the given function is even,odd,or neither.

A: To determine (algebraically) whether the given function is even, odd, or neither. f(x)=x1+x2

Q: Given that (1,-8) is on the graph of f(x), find the corresponding point for the function f(x).

A: According to question given that Corresponding point= (1,-8)from above data we know that f(1)=-8This…

Q: If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x)/g(x). %3D…

A: here f(1)=2,g(1)=1,f(5)=3,g(5)=2 Lets find f'(1),g'(1),f'(5),g'(5): for 0≤x≤2…

Q: Let f(x) = 3|x| If g(x) is the graph of f(x) shifted right 1 units, write a formula for g(x) 9(x)=|

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Q: Express the function,h(x) =1/(2x - 3) as a composition of two functions f and g so that h(x) = (f ∘…

A: We will take the inner function as g(x) and the outer function as f(x). Note that 2x-3 is inside.…

Q: Express the function,h(x) = |3x - 4|as a composition of two functions f and g so that h(x) = (f ∘…

A: h(x) = |3x - 4| To write h(x) as a composition of two functions f and g so that h(x) = (f ∘ g)(x)…

Q: Without graphing, compare the graphs of the indicated functions from the given function. 3. f(x) = *…

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Q: If f and g are both even functions, is f + g necessarily even? If both are odd, is their sum…

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Q: Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F and G are the functions whose graphs are shown. 1

A: We have to use chain and quotient rule.

Q: Sketch the graphs of the following functions. (a) f(x) = x2   (b) g(x) = x3    (b) h(x) = √x

A: Graph of fx=x2 We have f-x=-x2=x2 Graph is symmetric about y-axis.

Q: Let f(x) 4 = x If g(x) is the graph of f(x) shifted left 2 units, write a formula for g(x) g(x)=

A:

Q: A function  f is defined by f(x) = { 1-x     , if x<=1            x^2    , if x>1 Evaluate…

A: The given function is fx=1-xif x≤1x2otherwise.   Note that 0 and 1 satisfies the condition x≤1.…

Q: f

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Q: If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x)/g(x). %3D

A: Given data:   The expression for the first function is u(x)=f(x)g(x). The expression for the second…

Q: Find all values of x such that f (x) > 0 and all x such that f (x) < 0, and sketch the graph…

A: Find all values of x such that f (x) > 0 and all x such that f (x) < 0, and sketch the graph…

Q: find (f◦g)(x) and (g◦f)(x) for the pair of functions and give their domains.  f(x)=1/x^4, g(x)=4-x

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Q: Assume that (a, b) is a point on the graph of f. What is the corresponding point on the graph of the…

A: Given a,b is point on the graph y=fx. Now, we know that graph of y=f-x is the reflection of graph of…

Q: Find f^-1 (x), if it exists, and graph both f(x) and f^-1 (x). f(x)= ((x+1)/(x))

A: Find f^-1 (x), if it exists, and graph both f(x) and f^-1 (x).  f(x)= ((x+1)/(x))

Q: draw the graphs of each of the piecewise-defined functions.

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Q: In the given question, , use a graphing utility to graph the function and find the x-values at which…

A: Consider the function  f(x) = x2/5

Q: The parent function f(x)=x3 is related to g. Use function notation to write g in terms of  f.…

A: The parent function f(x)=x3

Q: The parent function f(x)=x² is related to g. Describe the sequence of transformations from f to g.…

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Q: Given the function f" (x) = directly from the sign chart of the given function about the graph of f…

A: Consider the given function.

Q: Jx + 2 if x -1

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Q: If f -1 denotes the inverse of a function f then the graphs of f and f-1 are symmetric with respect…

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Q: Given the graphs of f(x) and g (x) below, find the composition of functions f(g(2))

A: Given,            The graphs of f(x) and g (x) shown below:

Q: Consider the following function. f(x) = x4 + 4x3 + 12 (a) Make a sign diagram for the first…

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Q: Use transformations of the graph of​ f(x) =x2 to determine the graph of the given function.…

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Q: Let f(x) = 3/a. If g(x) is the graph of f(x) shifted up 5 units and left 1 units, write a formula…

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Q: Let f(x)= X-4. Sketch the graph of f and f and find the rule of f-1. 2.

A: We have to sketch the graph of the function fx=12x-4 and its inverse, also find the inverse of the…

Q: Let f(x) = x³ If g(x) is the graph of f(x) shifted up 1 units, write a formula for g(x) g(x)=

A: Consider the function  f(x)=x3

Q: Consider the following. f(x) = (x + 4)? (a) Sketch a graph of the function f.

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Q: Let f(x) be the following piecewise-defined function -x3 – 6, x 2 (a) Sketch the graph of f(x).…

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Q: Let f(x) = 3/ If g(x) is the graph of f(x) shifted down 2 units and left 3 units, write a formula…

A: Given function is f(x)=3x We know that if graph of f(x) is shifted h units to the left and and k…

Q: Sketch the graph of the following piecewise -defined function by plotting points: f(x) = {x +2x if x…

A: we have to draw by put some value of x and get f(x)

Q: Use transformations of the graph of f(x) = x to determine the graph of the given function. h(x) = -…

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Q: If h(x) 6.x + 1, find h(). Is h a one-to-one function?

A: If h(x) = 6x +1. To find h(1/2). Also, to check whether h is a one-to-one function.

Q: Use the graphs of f and g to evaluate the functions:

A: 7.a f(1) = 2 g(1) = 3 (f -g)(1) = f(1) - g(1) = 2 - 3 = -1 Therefore (f -g )(1) = -1

Q: Use the graphs of f and g to evaluate the function. = g(x)

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Q: Find all values of x for which the graph of f lies above the graph of g.f(x)=1/x, g(x)=1/x-1

A: Given: f(x)=1xg(x)=1x−1

Q: The parent function f(x)=x³ is related to g. Use function notation to write g in terms of f. g(x)=…

A: Given two functions, f(x)=x3 & g(x)=(x-1)3+1 We need to write g(x) in terms of f(x).

Q: Describe a function g(x) in terms of f(x) if the graph of g is obtained by reflecting the graph of f…

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Q: Given below are the graphs of the functions f(x), g(x) and h(x).

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Q: Let f(x)=4|x| If g(x) is the graph of f(x)shifted left 5 units, write a formula for g(x) g(x)=

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Q: Express the function,h(x) = (2x - 5)3 as a composition of two functions f and g so that h(x) = (f ∘…

A: Given, hx=2x-53

Q: Z-3 f(2) = (z – 3)(x – 1)

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Without graphing, compare the graphs of the indicated functions from the given function. 3. f(x) = *…

A:

Q: Let f(x) be a one-to-one function with the point (-1,2). If f'(-1) = 12, then find f-1(2)

A: fx be the one-one function having the point -1,2 and f'-1=12. So the inverse function is f-1(y)=x if…

Q: 3-f(x)=

A: Explanation of the answer is as follows

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.