7. For the following function: f (x) = 2 log3 (2x + 3)- 4 state:a. the transformations applied to the base (parent) function:y = log3 xb. the domain%3D4.c. interceptsd. asymptotes,Sketch a well labelled graph using the intercepts and theasymptotes.5.6.7.

a) To find domain, intercepts, and asymptotes of the given function, and to draw its graph.…

Answered: 7. For the following function: f (x) 2…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Graph the function f (x) must plot the asymptote and any two points with whole number coordinates. = -3 log2 (-x – 7) + 4 on the axes below. You Asymptote: 12 11 10 9. 8 7 6. 4 3 10 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 8. 1 2 3 4 7 9. 10 11 12 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12
What is the equation for the horizontal asymptote of the graph of the function shown? O O I 84 0 4 y = 4 y = 2 x = 2 y 8 x = 4 -8 I I 8
3. a. What is the domain of the function g(x) ? Write the answer in interval notation. g(x) = log₂ (x-3) +4 b. What is the range of g(x)? c. List the transformations on y = log 2 x to obtain g(x) and Graph g(x) by following the transformations. The graph of log2 x is given below.
1. Complete these tasks for each of the following functions. i. Describe the transformations of the function f(x) = a(c)b(x-h) + k that occurred. ii. Sketch the graph of the function. iii. Identify the domain, range, equation of the horizontal asymptote, and intercepts. a. y == 12 x+2 -3 16 14 12 10 8 6 4 2 20 -18 -16 -14 -12 -10 -8 -6 -4 -2 2 4 6 8 10 12 14 16 18 20 -2 -4 -6 -8 -10 -12 -14+
7. Find the following information for each function. (1) State the domain (in interval notation). (ii) Find the equation(s) of the vertical asymptote(s). (iii) Find the x-intercept(s). (iv) Find the y-intercept(s).
2. Given g(x) =- ft(* - 3)) – 5where f(x) = 2" a. Write the equation of the transformed function b. Graph the transformed function. Be sure to show all steps! c. State the domain ana range of the function -10

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7. For the following function: f (x) 2 log3 (2x + 3) – 4 state: a. the transformations applied to the base (parent) function: y = log3 x b. the domain C. intercepts d. asymptotes, Sketch a well labelled graph using the intercepts and the asymptotes.