Consider the quadratic function: f(x)=2x^2−8x+2 . Find the following for this parabola. A) The line of symmetry: B) The vertex: C) The vertical intercept is the point D) Give the coordinates of the two xx intercepts of the parabola as ordered pairs.
The function f is defined as follows. f(x)- 4x-3 if x21 (a) Find the domain of the function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. (e) Is f continuous on its domain?
The function f is defined as follows. f(x)- 4x-3 if x21 (a) Find the domain of the function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. (e) Is f continuous on...
7. Given f(x)=_x - 2x x--3x-4 a. Why does f define a function? b. Find Dom fand Range f. c. Graph y = f(x) in detail. Include intercepts, symmetry, and asymptotes, including limit behavior for the asymptotes. d. Find the point where the graph crosses the horizontal asymptote.
For the indicated function, find the values f(-9), f(0), and f(4). x, if x < 0 f(x)= 8x + 6, if x 20 f(- 9) = f(0) = f(4) = State whether f(x) has a maximum value or a minimum value, and find that value. f(x) = 2x² - 4x - 6 The function has a value of Graph the case-defined function and give the domain and range x+2 xs2 f(x)= Choose the correct graph of the function below. OA...
Find the absolute maximum and minimum of the function f(x,y)=2x? - 8x + y2 - 8y + 7 on the closed triangular plate bounded by the lines x = 0, y = 4, and y = 2x in the first quadrant. On the given domain, the function's absolute maximum is The function assumes this value at . (Type an ordered pair. Use a comma to separate answers as needed.) On the given domain, the function's absolute minimum is The function...
11. For parts (a-c) consider the polynomial function(x) = -2x²(x - 4)'(x - 1)*(x + 2). [10 Points) (a) What is the degree of the polynomial function? (b) List the zeros of the function in the table provided below and state the multiplicity of each zero. Describe the behavior of the graph at each of the zeros. Does the graph Touch/Cross at each zero? Zero Multiplicity Touch/Cross of 2 -6 -4 -2 -21 (c) Provide a rough sketch of the...
For the polynomial function f(x)=x^4+8x^3+16x2 answer the following: A. Using the leading coefficient test , determine the graphs end behaviour. B. Find the X-intercepts and at which x-intercept does the graph cross the x-axis? C. At which x intercepts does the graph touch the x axis and turn around? D. What is the y intercept? E Determine whether the graph has y axis symmetry, origin symmetry or neithr. F.If necessary, find a few additional points and graph the function. Use...
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y = f'(x) (c) state the domain of f and the domain of f. Find lin tan 4x cos 3x sin 5x X> 12 Find y if y = (3x+5)*(x+4x) (3 Find y' it ya + 10x tanx 7 Let y= (a) Find (6) Find the equation of the tangent line at (74 y' Elf 8 X3 Prove lim (5-) = 4 (a) write the...
Question 4 (2+4+4+1+4 = 15 marks) Consider the function y = 4 sin (2x-π) for-r below to sketch the graph of y. x < π. Follow the steps (a) State the amplitude and period in the graph of this function 4 sin (22-9 ) for-r (b) Solve y π to find the horizontal intercepts x (a-intercepts) of the function. (c) Find the values of x for-π π for which the maximum. and the x minimum values of the function occur...
Include all relevant work please.
s. Consider f(x) = *** a. Find the domain. [3] b. Find any vertical asymptotes. [3] c. Determine if there are any holes. If so, give the coordinates of the hole. [2] d. Find any horizontal or oblique asymptotes. [3] e. Determine if the graph intersects a horizontal/oblique asymptote, if it exists. Show work! [3] f. Sketch a graph of the function. To receive full credit, label any x and y intercepts and the asymptotes....