Find a function f for which fx 3 is not equivalent to fx f

Find a function f for which f(x + 3) is not equivalent to f(x) + f(3). Then find an f for which f(x + 3) is equivalent to f(x) + f(3). 602 Draw a picture of the spiral r = 3^theta/720 in your notebook. Identify (and give coordinates for) at least four intercepts on each axis. 603 If P(x) = 3(x + 1)(x - 2)(2x - 5), what are the x-intercepts of the graph of y = P(x). Find an example of an equation whose graph intercepts the x-axis only at -2, 22/7, and 8. 604 The x-intercepts of y = f(x) are -1, 3, and 6. Find the x-intercepts of (a) y = f(2x) (b) y = 2f(x) (c) y = f(x + 2) (d) y = f(mx) Compare the appearance of each graph to the appearance of the graph y = f(x). 605 Some functions f have the property that f(-x) = f(x) for all values of x. Such function is called even. What does this property tell us about the appearance of the graph of y = f(x)? Show that C(x) = 1/2(2^x + 2^-x) is an even function. Give other examples. 606 Let the focal point F be at the origin, the horizontal line y = -2 be the directrix, and P = (r, theta) be equidistant from the focus and the directrix. Using the polar

Solution

x intercepts of y= f(x) are x =-1 ,3 and 6

Now,

a) y = f(2x)

x intercept would be shrink by 2 .So, x = -1/2 , 3/2 , 3

b) y = 2f(x)

No change x =-1 ,3 and 6

c) y = f(x+2)

x intercepts get shifted to left by 2 units

x = -3 , 1 , 4

d) y = f(mx)

x intercept would be shrink/expand by m units .So, x = -1/m , 3/m , 6/m