Suppose the following is the graph of a function f(t). Match the given functions (a)-(f) woth the...
Consider the function below. y z= 2+x+ (a) Match the function with its graph (labeled A-F). (b) Match the function with its contour map (labeled 1-VI). O V VI Give reasons for your choices. Select- Also, the values of z approach 0 as we use This function is not periodic, ruling out the graphs in (b) Match the function with its contour map (labeled I-VI) II III IV V VI Give reasons for your choices. This function is not periodic,...
QUESTION 2 Given two periodic functions, f(t) and g(t) is defined by and f (t) = cos, -<t<t f(t)= f(t +26) g(t) = cos, 0<t<2n g(t) = g(t +21) Sketch the graph of the periodic functions f(t) and g(t) over the interval (-37,37). Sketch in separate graphs. (Please use any online graphing software not hand-drawn). Find the Fourier series of f(t) and g(t). (b) Then, briefly comment what do you observe from the graphs and the Fourier series expansion of...
3. Below you are given the graphs of the functions f and g. Suppose that: u(x)-f(g(x)), v(x)-f(x) g(x), and w(x)-g(f(x)) Use the graphs to find the indicated derivatives. If the indicated derivative does not exist, write "D.N.E." in the space provided. Be sure to include work that shows how you arrived at your answer. 20 a) u'3) b) v-4) c) wl) 3. Below you are given the graphs of the functions f and g. Suppose that: u(x)-f(g(x)), v(x)-f(x) g(x), and...
1. In each of the following piece-wise functions: (i) Sketch the graph of the given function, (ii) Express f(t) in terms of the unit step function uc(t) = u(t -c) where 0 u(t) = t<0 t> 0 and (iii) find the Laplace transform of f(t). (a) $(t) = { 2=(1-2), 0<t<2 t> 2 (b) f(t) = t, 2, 7-t, 0, 0<t <2 2 <t<5 5<t<7 t> 7
Problem #9: The graph of f(t) is given below. 5 4 3 2 2 10 4 -1 1 (a) f() can be represented using the following combination of Heaviside step functions а U(t - 3) + b U(t - 4) + с U(t - 9) Enter the constants a, b, and c (in that order) into the answer box below. (b) Find the Laplace transform F(s) = Pf()} for s 0. a, b, c (in that order), separated with commas....
Question #5 Evaluating Function Operations Reference Q. 11168 The graph of two quadratic functions, y=f() and y=g(x), ER are shown on the grid. a. Use these graphs to sketch the graphs of y=(1-9)() and y=(9-f)(x) for IER. b. How do the graphs of y=(f -9)(x) and y = (9-) (2) relate to each other? 2.0 + 2. Write expressions for the c. The functions f and g above are f(x) = 2x? - 2 - 8 and g(x) = -12...
4. Consider the graph of the function f shown below. Use this graph to sketch the graphs of the following functions. To print an enlarged copy of the graph, go to the website www.mathgraphs.com (a) f(x) (c) 2f(x) 4 (d) fx) (f) f(x) (e) -f() (g) f(x) 2 4 -2 -4
2. The graph of u = f(t) is given. (a) Graph A(a), B(x) and C(a) on the grids provided 11 T 후-; A(z) = /(x)--2 13(z) = f(x-1) (b) Evaluate the following (use the formulas given and the graph of the parent func A(o) B (1) = C(1) = (a) Give the domain and range of the parent function u = f(t). Domain: Range: (b) Give the domain and range of the transformed function C(x) = f(x-1) +2. Domain: Range:
The function f(x) is given by the graph below: (a) Write a piece-wise formula for f(x): (b) Determine if each of the following graphs are simple (single shifts, scalings, or reflections) transformations of f(x). If it is, write a formula for the graph in terms of f. Otherwise, explain why it is not The function f(x) is given by the graph below: (a) Write a piece-wise formula for f(x): (b) Determine if each of the following graphs are simple (single...
2. Sketch the graph of each of the following functions, and determine whether the given function is one-to-one. Show your work! (a) f(x) = -|x +31 – 2 (b) g(x) X + 3 X + 2