2. Sketch the graph of each of the following functions, and determine whether the given function...
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. 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
g) Sketch the graph of f(x) h) Determine the minimum or maximum value of the function. i) State the domain and the range in interval notation. 1. Given f(x)-2-3x (7 points) a) State whether the graph of the parabola opens upward or downward. b) Identify the vertex using the vertex formula. c) Determine the x-intercepts d) Determine the y-intercept. e) Determine the axis of symmetry ) Write the equation of the function fit) in vertex forrm g) Sketch the graph...
The functions fand g are given. Find each of the following functions and determine their domain. (Enter your answer for each domain using interval notation.) (x) = 3x + 4 and g(x)=2x-3 (a) (f+)x) function (f+)() - domain (b) (- 9)x) function (f - 9)x) = domain C) (f. 9x) function (f)(x) = domain function domain
Consider the given function f(x) = 19 4 (a) Determine whether the graph of the parabola opens upward or downward. (b) Identify the vertex. (c) Determine the x-intercept(s). (d) Determine the y-intercept(s). (e) Sketch the function. (1) Determine the axis of symmetry. (9) Determine the minimum or maximum value of the function. (h) Write the domain and range in interval notation. Write your answers in exact form. Part: 0 / 9 Part 1 of 9 (a) Determine whether the graph...
(a) Determine whether each of the following functions is uniformly continu- ous on the given domain. Justify your answer in each case. (i) f(x) = log (2 + cos(e«)) on R. (ii) g(x) = Väsin ( sin on (0,1).
Sketch the graph of a function g that satisfies the given conditions Problem 7. Sketch the graph of a function g that satisfies the siven conditions a. Iin, g(z)=4 b, g(-6)=2 d, lim g(z)=4 e, lim g()-2 -40 lim olr) exists, but g is not continious at 4 10 g is continnons at r6 Problem 8 (Bonns). Show that at this moment there are two places on opposite sides of the earth where the temperature is exactly the same Problem...
1) Sketch the graph of each of the following exponential functions. Make sure you label at least three points on the graph or include a t-chart with the coordinates. a. S(x)=3 b. y=213 c. g(x)= (3) 3 d. y e. f(x) = "+1
Sketch a possible graph of a function that satisfies the conditions below. Determine whether fis continuous at x = 1. f(1) = 2; lim f(x) = -2; lim f(x) = 2 x=1 *1* Choose the correct graph below. OA. B. OC. D. ro х X х -5 5 -5 5 -5 5 -5 5 Is f(x) continuous at x = 1? No оо Yes
Sketch a graph of the following functions; assume that x is in degrees and be sure to label your axes. Additionally, give their midline and amplitude. (A.) f(x) = 3 cos(x) — 3 (B.) g(x) = sin(x) + 2 (c.) h(x) = 5 cos(x) – 7 (n.) p(x) = sin(x) + 3