1. For the function ?(?)=−3(?−1)^2+5, choose a domain restriction to make ?(?) a one-to-one function, and...

1. For the function ?(?)=−3(?−1)^2+5, choose a domain restriction to make ?(?) a one-to-one function, and then find the inverseof ?(?).

2. For the following function, find the horizontal and vertical asymptote(s):?(?)=3?^2+3?−18 /?^2+5?+6

3. Find the inverse function for ?(?)=4? / 5−3?

4.Find all zeroes (including complex ones) for the following function without using a graph:?(?)=?^4+5?^3+4?^2−7?−3

Expert Solution

milcah answered 2 years ago

5. Consider the function f(x) = -x^3 + 2x^2 + 2. (a) Find the domain of...

5. Consider the function f(x) = -x^3 + 2x^2 + 2. (a) Find the domain of the function and all its x and y intercepts. (b) Is the function even or odd or neither? (c) Find the critical points, all local extreme values of f, and the intervals on which f is increasing or decreasing. (d) Find the intervals where f is concave up or concave down and all inflection points. (e) Use the information you have found to sketch...

5. For the function ?(?)=−3?^4 −12?^3 Find the domain and intercepts. Find the critical numbers, intervals...

5. For the function ?(?)=−3?^4 −12?^3 Find the domain and intercepts. Find the critical numbers, intervals where f (x) is increasing and decreasing, and any local maximum and local minimum points (find both coordinates). Find the intervals where f (x) is concave up and concave down and any inflection points (find both coordinates). Use this information to sketch the graph of f (x).

5. Given the function y = q(x) = (x^2)/(x-1) a. What is the domain of q(x)?...

5. Given the function y = q(x) = (x^2)/(x-1) a. What is the domain of q(x)? b. What are the vertical asymptotes? c. What are the horizontal asymptotes? d. Where is q(x) increasing/decreasing (draw a line and specify by intervals – be sure to include points where q isn’t defined)? e. Where is q(x) concave up/down ((draw a line and specify by intervals – be sure to include points where q isn’t defined)? f. Find rel max/min. g. Find inflection...

The function f(x)=3x+2 is one-to-one a) find the inverse of f b) State the domain and...

The function f(x)=3x+2 is one-to-one a) find the inverse of f b) State the domain and range of f c) State the domain and range of f-1 d) Graph f,f-1, and y=x on the same set of axes

1.Suppose you have a function such that the domain of is −4≤x≤2 and the range of...

1.Suppose you have a function such that the domain of is −4≤x≤2 and the range of is −1≤y≤6. a. What is the domain and range of the transformation f(2(x+3))? b. What is the domain and range of the transformation 2f(x)−3? c. How do you know your answers are correct? d. What can we say about how transformations affect the domain and range of a function? 2. Suppose a local vendor charges $2 per hot dog and that the number of...

1) Find the domain and range of the rational function y( x) = x^2-25 / 2x^2...

1) Find the domain and range of the rational function y( x) = x^2-25 / 2x^2 + 13x+15 A) Factor the numerator and denominator B) Determine the point of discontinuity if it exists.

Consider the following function ?(?) = ?^ 4+ 2? ^3 + 8?^ 2+ 5? With the...

Consider the following function ?(?) = ?^ 4+ 2? ^3 + 8?^ 2+ 5? With the initial guesses of ?1 = −2, ?2 = −1, and ?3 = 1, find the minimum of the given function using parabolic interpolation. Perform five iterations, reporting Ɛa based on the location of the minimum (i.e. xopt) and not the actual minimum value. (Round the final answer to four decimal places.)

Direction ratio of line joining (2, 3, 4) and (−1, −2, 1), are: A. (−3, −5, −3) B. (−3, 1, −3) C. (−1, −5, −3) D. (−3, −5, 5)

Direction ratio of line joining (2, 3, 4) and (−1, −2, 1), are:A. (−3, −5, −3)B. (−3, 1, −3)C. (−1, −5, −3)D. (−3, −5, 5)

Find the domain of the function g(x) = square root of 3x+3

The domain of the function h(x) = ln(x + 3) + x2 − 4 is (A)...

The domain of the function h(x) = ln(x + 3) + x2 − 4 is (A) {x∈R| −3<x<−2or−2<x<0} (B) {x∈R| −3<x<−2or−2<x≤0} (C) {x∈R| −3≤x<−2or−2<x≤0} (D) {x∈R| −3<x<−2or0≤x<2} (E) {x∈R| −3<x<−2or(x≥0andx̸=2)} (F) None of (A) - (E)

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