Determine whether the functions are even/odd/neither and state what that would m

Question

Determine whether the functions are even/odd/neither and state what that would mean about the graph of the function f (x) = 2x/x^2 + 1 f (x) = |x| - x^2 if (2, -3) is on the graph of y = f (x), find the corresponding point on the graph of y = -3 f (-5x) -2 y = 1/2 f (x - 5) + 2 Find the equation of the function g (x). given that it is a transformation of the graph of y = |x| Find formula for a function g(x) whose graph is obtained from f (x) = squareroot x by reflecting across the y-axis stretching horizontally by a factor of 2 and shifting down 3 units shrinking vertically by a factor of 1/2 reflecting across the x-axis, and shifting right 3 units and up 4 units. Sketch the graph of f (x) = -3|x - 5| + 2 and determine the domain of f the range of f interval(s) on which f is inc/dec/constant local max/min and absolute max/min Find the equation (in slope intercept form if possible) of the line: passing through (-2, 2) and (1, -3) passing through (-2, -3) and (l.-30) passing through (5, -4), parallel to the line y = -4/3 x - 3 passing through (5, -4), perpendicular to y = -1, Find the value of k, that the line containing the points (k, 2) and (2-2) perpendicular to the line containing the points (-5.3) and (0, 7) A cable company charges a $20 installation fee and $55 per month of service. Write a function for C(t) that represents the total cost of t months of cable service What is the total cost for 6 months of services? What is the domain of C(t)? What is the range of C(t)? Find the equation of the line graphed below:

Explanation / Answer

3. a function f(x) is odd if f(-x) = -f(x)

a function f(x) is even if f(-x) = f(x)

that is an even function's graph is symmetric about the x axis

and an even function's graph is symmetric about the y axis

i> f(x) = 2x/(x^2+1)

f(-x) = -2x/((-x)^2+1) = -2x/(x^2+1)

hence f(-x) = -f(x)

therefore f(x) is an odd function and its graph will be symmetric about the x-axis.

ii> f(x) = |x| - x^2

f(-x) = |-x| - (-x)^2 = |x| - x^2

=> f(-x) = f(x)

Hence f(x) is an even function and the graph of f(x) is symmetric about the y-axis

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