9. (4pts) Consider the linear functions f(x) 6-x+3(x-4) and g (x)-3(x+)-5(+1). Solve f(x) g() algebraically, showing...
Graphs of fand g are shown. AK Is feven, odd, or neither? even odd neither Explain your reasoning. It is symmetric about the origin. It is symmetric with respect to the y-axis. It is symmetric with respect to the x-axis. It is not symmetric about the origin or the y-axis. Is geven, odd, or neither? even odd neither Explain your reasoning. It is symmetric about the origin. It is symmetric with respect to the y-axis. It is symmetric with respect...
Determine algebraically whether the function is odd, even, or neither. g(x) = -5x4 - 3x2 +9 O Odd, g(-x) = -g(x) O Even, g(-x) = g(x) Odd, g(-x) = g(x) O Neither even nor odd Even, g(-x) = -g(x)
(a) Determine algebraically whether the functions below are even, odd or neither. i. r+6 f(x)=- r-r? (2 marks) ii. f(x) = 2x sinx (2 marks) (b) A periodic function is defined by: f(x) = 4-x?, -25x52, f(x+4)= f(x) i. Sketch the graph of the function over -10<x<10. (4 marks) ii. Based on result in (i), identify whether the function is even or odd. Give your reason. (2 marks) ii. Calculate the Fourier series expansion of f(x). (12 marks) (c) An...
Odd and Even Functions An even function has the property f(x) =f(-x). Consider the function f(x) Now, f (-a)-(-a)"-d f(a) An odd function has the property f(-x)-f(x). Consider the function f(x) Now, f (-a) = (-a)' =-a3 =-f(a) Declarative & Procedural Knowledge Comment on the meaning of the definitions of even and odd functions in term of transformations. (i) (ii) Show that functions of the formx) are even. bx2 +c Show, that f(x) = asin xis odd and g(x) =...
3. Determine algebraically whether each of the following functions is one-to-one. Show your work! (a) f(x) = 4x2 4x (b) g(x) 3x + 2 2x – 1
1. 6 marks] Sketch the following functions on the interval x E -2,2] and determine (state) whether they are even, odd or neither. In each case you should give your reasoning (a) f(x)-İr'l (b) h(x)-2x+x2
answer all and show work please. clear hand writing please 1. (6 points) Let f(x) = -x2 - 2x + 3. (a) Does the graph of f(x) open upward or downward? Justify your answer. 6) Algebraically find the vertex and axis of symmetry of f(x). Report each answer as an ordered pair and equation, respectively, Vertex Axis of Symmetry: (C) Algebraically find the X- and y-intercepts of f(x). Report your answer(s) as an ordered pair(s). x-intercepts: y-intercept: (a) Using parts...
4. Below is a piecewise function, determine -5 lim,f(x)= c, lim f(x)= e. lim f(x)- d. y = sin x (not drawn to scale) explain Consider the piece of f(x) in the first quadrant resembling e. Determine lim sinand the behavior of the graph near zero. 5. Using your graphing calculator sketch h(x)-x4-2x3 over [-2,2] below, find the critical values and on the graph label the coordinates of any local, global(absolute) minima, maxima or point of inflection on the sketch,...
We've been using L'Hopitals as well as family of functions and modeling. stuff from chapter 4 in the 7th Edition of single variable calculus book. 1. (7 points) A rectangle is located with its base along the x axis, one corner at (8,0) and the opposite corner on the graph y = ln(x) for some 1 x 10. Draw a picture of the given scenario. a. If the other corner along the x axis an x value of e, what...
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)...