State the transformations that have been applied to log3 x to obtain f (x) = -2 log3[2x – 6] – 4 Sketch the original and J (x) (Clearly label key point(s) and the asympto

Q: 6. The logarithmic function f(x) = In(x – 1) has the asymptote x %3D

A: Given, Logarithmic function, f(x)=ln(x-1)

Q: 2 Find x so that log10 x = log, 10

A:

Q: The parent function f(x) = log3x has been transformed by reflecting it over the x-axis, stretching…

A:

Q: Prove that In x lim I xP for any number p > 0. This shows that the logarithmic function approaches o…

A: Given

Q: 2. Find the domain. (a) f(x) = log2(log3 x) (b) g(x) = log [In(x – 1)] (c) h(x) = In [log(x – 1)]…

A: Domain.

Q: Sketch the graph of the function by plotting points. f(x) = log2(x) f(x) = log,(x) 22 y y 4 4 2 4 6…

A: We need to sketch the graph of the following function fx = log2x

Q: The parent function f(x) = log4x has been transformed by reflecting it over the x-axis, stretching…

A: We will find the trnasformed function as following.

Q: log(2² – 2y² – 4x²) In(2 – |2|) - g(x, y, z) = -

A:

Q: Find the equation of the vertical asymptote f(x) = log(x – 1)

A:

Q: Find the equation of the vertical asymptote f(x)=log(x+5)

A:

Q: 2. The function f(x) = log, x is the logarithm function %3D So f(9) = -- f()- with base %3D f(1) =…

A:

Q: () N f(x) = , show that f(0) and its leading differences form a geometr 5. (i) Prove that A log x…

A:

Q: Consider the function g defined by 1 g(x, y) = cos (Tx)+ log3 (x - y) Do as indicated. 1. Determine

A:

Q: Sketch the graphs of ƒ(x) = log2 (x) and g(x) = −log2 (x) in the coordinate plane.

A: Graph of logarithm

Q: Find the equation of the vertical asymptote f(x) = log(x + 5)

A:

Q: How is the graph of y =log(x) transform to produce the graph of y=log(2x)+3

A: Given graph of y = log(x), transform it to get the graph for y = log(2x) + 3.Let us first discuss…

Q: sketch the graph of f(x) =1 log2 (x+3)  state vertical shift, horizontal shift, ordered pair where…

A: The given function is f(x) =log2 (x+3)To sketch, state vertical shift, horizontal shift, ordered…

Q: 1. Find the function of the form y = log,(x) whose graph is given. y = y 1.5 (5, 1) 1.0 0.5 5 6 -0,5…

A:

Q: Choose the graph that shows the transformation of f(x) = log(a) shifted 1 units to the left and…

A:

Q: Find the equation of the vertical asymptote f(x)= log(x+1)

A: The equation of the vertical asymptote f(x)= log(x+1)

Q: The natural logarithmic function f(x) = In x has the asymptote x =

A: Given: f(x)=lnx To Find: Asymptote of f(x). Concept: Vertical Asymptote: x=c is called vertical…

Q: Q 3/ A- Find lim,3 B- log10 (3x – 7) + log10(3x + 1) = 1+ log10 2

A:

Q: 54. For any positive constant k, the derivative of In (kx) is 1/x. Prove this fact (a) by using the…

A: Given for any positive constant k, the derivative of ln (kx) is 1/x. To prove that  a) by using the…

Q: - Use the fact that d In x/dx = 1/x, as well as the change-of-base theorem for logarithms, to prove…

A: Given : d lnxdx = 1x d logaxdx = 1xlna

Q: a) Express the new function h(x) = log2(x + 2) in terms of the original function f (X) = log2(x).…

A:

Q: Prove that In x lim xP for any number p > 0. This shows that the logarithmic function approaches…

A: Prove that limn→∞ ln xxP=0for any numbers P>0

Q: For the function f(x)=5.log (x* - 10x +x+30)-5, on the interval (-4, 4), approximate the local…

A:

Q: 1+x2 Through the proof of the logarithmic form of the function y-cschx-In(- |x| which of the…

A: The logarithmic function is the inverse function of the exponential function. The logarithmic…

Q: The logarithmic function f(x) = In(x – 1) has the asymptote x =

A: Given: fx=lnx-1 we know that lnx has the vertical asymptote x=0 similarly, given function has the…

Q: 5. Sketch a graph of the function f(x) = 3 log(2x – 2) +4. Identify the key features. a) domain and…

A: The given function is: fx=3log2x-2+4 The logarithm is defined only for positive real number.…

Q: -, State the transformations that are needed to turn y 4 log10(x – 4) into y = – 2 log10(x + 1).

A: Compare the both equation and take transformation and varify

Q: State the transformations that have been applied to log3 to obtain f (x) = -2 log3[2x – 6] - 4

A:

Q: Find the exact x-coordinate where there is a horizontal tangent line to the graph of f(x) = x8*.…

A: To find the exact x- coordinate.

Q: Choose the graph that shows the transformation of f(x) = log(x) shifted 2 units to the left and…

A: We will use the transformation of graphs to find the transformed result :  To shift the graph left…

Q: Find the domain of the function. f(x)= log %3D

A:

Q: What transformations would map the graph of f (x) = log3 (a) onto the graph of g(x) = log3 (81z³)?

A: Given data fx=log3x gx=log381x3

Q: If f(x) = log2x then which function below has been vertically stretched, %3D shifted right 2, and…

A: Answer: C)2f(x+2)-1

Q: b. y= tan(7x-3)•log 4(5 + 2x) use the Product rule (3)

A: We use product rule of derivative :d/dx(uv)=ud/dx(v)+vd/dx(u). See 2nd step.

Q: Find Y for the following function: dx 3- y = log,(x3- x) 4- y = In 5- tan-1 V4x – 5

A: we have to find the derivative of the following

Q: Given the function y=4 log(2x+1)+3 . State the domain, range and equation(s) of the asymptote(s) of…

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: The parent function h(x)= log3 (x) is tranformed into j(x)= 2 log3 (x + 3) – 7. Using complete…

A: Proceed as explained below...

Q: 5. The natural logarithmic function f(x) In x has the %3D asymptote x %3D

A: Given function - f(x) = ln(x)

Q: Which of the following transformations should be performed first when considering the graph of the…

A:

Q: direct

A:

Q: Find the domain of each fucntion: a.) f(x) = ln(2-x) b.) f(x) = log2(2x-3))

A: Calculation:Note that the argument of the logarithm function always positivea.) The domain of the…

Q: What is the equation of with the given transformations? Vertical compression by , left by 2 unit, up…

A:

Q: The natural logarithmic function f1x2  ln x has theasymptote x 

A: Graph of f(x):