Let f(x) = x* If g(x) is the graph of f(x) shifted up 4 units, write a formula for g(x) Preview =(x)6

Q: Find the value k that makes the function continuous. (ka?, x > -2 f (x) kx + 18, x < -2

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Q: Sketch the graph of f.

A: we have to sketch the graph of  the given function f(x)=log3(x2)

Q: Suppose the graph of f(x) = 1/xis stretched vertically by a factor of 4 and then shifted down 3…

A: Given function is fx=1x. We know that if graph of function fx is stretched vertically by c units…

Q: find The domain of tHhe function fCメ=-

A: This is a function with a square root, so we will be using the concept of square root function for…

Q: find the points of inflection and discuss theconcavity of the graph of the function. y=x-\ln x

A: Consider: y=x-ln x. Find the inflection points and concavity of function. First find the domain of…

Q: Find the formula for a function that has a vertical asymptotes x=4 and x=6 and a horizontal…

A: The easiest type of function to use for these types of problems are rational unctionsFor vertical…

Q: True or False The function f(x) = 2x/(x - 3) has y = 2 as a horizontal asymptote.

A: Given: fx=2xx-3 Concept Used: If degree of denominator is equal to the degree of numerator then…

Q: Suppose the function y = f(x) is increasing on the interval (−1, 5).• Over what interval is the…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: The graph of f (x) = |x| is reflected over the x-axis, shifted vertically up 1 unit, horizontally 3…

A: This question is based on transformation of graph.

Q: Find the value of the constant bl that makes the following function continuous on (-∞, ∞). if x 6|…

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Q: Sketch the graph of the function y=ln(x+1)−1.

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Q: Use the guidlines to sketch the graph of the function  y=1/x + ln x

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Q: Describe the behavior of the function h  around its vertical asymptote at x= -5 for the equation:…

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Q: Does y = e- - 2 exist? What is the domain & range of the function if it does exist?

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: The graph of f(x) and a line tangent to the curve at x = 4 are shown. If g(x) = f(x), evaluate…

A: Finding the g'(4) from the given conditions.

Q: Using the (e- 6) definition, show that f(x) = 3x – 1 is continuous at point x = 1.

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Q: Use a graph to explain why. if f is defined at x = a.

A: The given integral is ∫aafxdx Formula used: it is known that the area bounded by the graph of fx and…

Q: f(x) at x = - 3 X-3

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Q: Find the domain of the function g(x) = /1 – x ln x

A: We have to find domain

Q: Consider the graph of f' (x). At what value (or values) of x do f (x) have a local maximum?

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Q: Sketch the graph of f(x) = x lxl. Then show that f '(0) exists.

A: A function is a relation which maps each value in domain to exactly one value in range.  For a…

Q: Use the e - S definition to show that the function x- 1 f(x) = x +2 %3D is continuous at x = 3.

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Q: Find the domain of the function: f(x) = ln(4 - x)

A: we have to find the domain of the given function. f(x)=ln(4-x)

Q: Find the domain of the function: f(x) = ln(3 - x)

A: The Domain of a function Includes all values of x for which the function is defined. We know that a…

Q: 3. For what value of x does the graph of f (x) = e* – 2x have a horizontal tange

A: Solve the following

Q: Assume both the graphs of ƒ and g pass through the point(3, 2), ƒ′(3) = 5, and g′(3) = -10. If p(x)…

A: Given that the graphs of ƒ and g pass through the point (3,2). So, f3=2g3=2 Also, f'3=5g'3=-10

Q: . Sketch the graph of the unit step function, denoted by U and defined by U (x) = {0 1 if if x<0 0sx

A: Ux =0x&lt;01x≥0 So this step function is equal to 0 when time t is negative and is equal to 1 when…

Q: The location of the point of inflection in the graph of the function y = x ln x is

A: Given: y = x ln x

Q: does y=e9-x2-2 exist? whaet is the domain and range of the function if exists

A: Consider  y=e9−x2−2

Q: The graph of  f(x)  and a line tangent to the curve at  x = 4  are shown. If  g(x) = sqrt(f(x))…

A: In the question it is asked to calculate the value of g'(4) for g(x)=f(x). for the graph given…

Q: find f'(x) for f(x) = 2xtan-1 x - ln(1+x2)

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Q: Find the absolute maximum value of the function f(x) = 5(x - e

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Q: b. Use your calculator's TRACE function to estimate the x-values of any vertical asymptotes.

A: using trace function we have drawn the graph of the function.

Q: Find a formula for a function that has vertical asymptotes x = 3 and x = 9 and horizontal asymptote…

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Q: The graph of f(x) and a line tangent to the curve at x = 4 are shown. If g(x) = V f(x), evaluate…

A: To find: The value of g'(4) if g(x)=f(x). Concept used: Chain rule: f(g(x)=f'(x)g'(x)

Q: Graph the function y =x + 1                                      x2+1 by applying the first and…

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Q: Find the function f(x) given that f ′ (x) = e x + x and the graph of f passes through the point (0,…

A: Given: f'x=ex+x &amp; Px,y=0,3   As we know that; The Power rule: ∫xndx=xn+1n+1+C And…

Q: Find the specific that h (-3) =7 function satisfies hlx)こ 6-5x+x and

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Q: Find a formula for a function that has vertical asymptotes x = 6 and x = 8 and horizontal asymptote…

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Q: At what x value does the local maximum occur for the function x^3 -4x-2 ? Give your answer in…

A: It is maximum value problem.

Q: Q4:- Sketch the following functions showing the detailed steps in different graphs: h) f(x) = |Inx|

A: Sketch the following function showing in the given expression.  f(x) = 1/|lnx|

Q: Find the horizontal and vertical asymptotic for f(x)= 1/(1-x^2)

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Q: B1(a): Find the value of k that makes function continuous at x = 4 4x + 6 x > 4 f(x) = 6x – k x < 4…

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Q: Find the value for k so that the function will be continuous at x = -4. f(x) = 7x + 47 -x² + 18x81+k…

A: Topic = Functions

Q: The line tangent to the graph of f at x=3 is y=4x-2 and the line tangent to the graph of g at x=3 is…

A: Given that: The line tangent to the graph of f at x=3 is y=4x-2 and the line tangent to the graph of…

Q: Use the graph of the derivative g'(x) shown below and the terminology: increasing, decreasing, local…

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Q: Select all of the graphs that depict a function which is not differentiable at x=0.

A: Here, we need to select all the graphs that depict a function which is not differentiable at x=0.…

Q: Find the point on the graph of f(x) = Vx that is closest to the point (8, 0). (х, у) -

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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.