Question 12 (5 points) Consider the function f(x) = x2. Which of the following functions shifts...
consider Which function is the result of vertically stretching f(x) = x2 - 7 by a factor of 2 an translating it downward 5 units? OA) A) y = x² - 12 B) y = 2x2 - 5 OC) y = 2x2 - 12 OD) y = 2x2 - 2
consider Which function is the result of vertically stretching f(x) = x2 by a factor of 2 and translating it 4 units upward? O A) y= 2x² - 4 B) y = 2x2 + 4 C) y = -4x2 + 2 D) y = 4x2 + 2 Which function is the result of vertically stretching f(x) = x2 - 7 by a factor of 2 an translating it downward 5 units? OA) A) y = x² - 12 B) y...
Consider the following functions. f(x) = x2 + x, g(x) = x2 - 5 a) Find (f + g)(x), (f - g)(x), (f)(x), and (f/g)(x).(b) Find the domain of f + g. Find the domain of f- g. Find the domain of fg.
Show work thumbs up VII. Functions Find the Domain of each function. f(x)--/-x2-4x + 5 g(x)-In(4t-3) a) b) e) h(x)- +3x2 -x-3 Find the zeros, vertical asymptotes, and horizontal asymptotes f(x) = 3x"-14x-5 (4x-17x-15 6x2 -7x-5 f(x) = -12 万 b) Transformations a) Beginning with f(x)- Vx, find the function g(x) that shows fcx) shited to the let 2 units, reflected over the x-axis, and then shifted up 7 units. b) Beginning with f(x)find the function g(x) that shows f(x)...
1. State the domain of each function below (2.5 points each) Function f(x) = x2 f(x) = Domain f(x) = 1 f(ax)1 where b>0. State two facts that are true for ALL such functions regardless of the value of b. (10 points) 2. Consider the exponential function of the form f(x) Fact 1: Fact 2
x2 +7x+12 1. Consider the function: f(x)= x +3 a. Is this function continuous at x = -3? b. Does this function have a limit at x = -3? dito c. Is this function differentiable at x = -3? d. Sketch a graph of the function in the space below. Be sure to include all pertinent features.
3. Consider the function f(x) = x2 - 6x^2 - 5 a. Find the values of x such that f'(x) = 0. b. Use the results of part a to: find interval(s) on which the function is increasing and interval(s) on which it is decreasing. c. Find the value(s) of x such that f"(x)=0. d. Use the result of part c to find interval(s) on which f(x) is concave up and interval(s) on which it is concave down. e. Sketch...
(1 point) Consider the function f(x) = x2/5(x – 9). This function has two critical numbers A< B Then A = and B For each of the following intervals, tell whether f(x) is increasing or decreasing. (-0, A]: ? [A, B]: ? [B, 0) ? The critical number A is ? and the critical number B is ? There are two numbers C < D where either F"(x) = 0 or f'(x) is undefined. Then C= and D= Finally for...
Theoretical Part 1. Consider the problem of computing f(x)dx, where f(x) could be any function. Letting X1, X2 IID ~U[0, 2, define three very simple estimators: ff(0)f(2), i2= f(X1)f(X2), fi3 = f(X1/2) + f((X2+2)/2) (a) (5 points) Is ft an unbiased estimator of u? (b) (5 points) Is i2 an unbiased estimator of ? (c) (5 points) Is 3 an unbiased estimator of ? (d) (10 points) Compute the variance of each of the three estimator when f(x) x Theoretical...
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...