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(a) Determine the intercepts. (b) Based on the graph, tell whether the graph is symmetric with respect to the x-axis, the y-axis, and/or the origin. (c) Based on the graph, tell whether the function is even, odd. or neither. (d) List the intervals on which ſ is increasing. List the intervals on which fis decreasing. (e) List the numbers, if any, at which f has a local maximum value. What are these local maxima values? (f) List the numbers, if any, at which f has a local minimum value. What are these local minima values?

a Determine the intercepts b Based on the graph tell whether the graph is symmetric with respect to the xaxis the yaxis andor the origin c Based on the graph te class=

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Problem

Solution

Part a

For this case the x intercepts are:

(-5,0) , (-1,0) and (5,0)

The only y intercept is given by: (0,-3)

Part b

For this case we can see that f(x) =-f(x) for one of the side sof the graph so then we can conclude that the graph is symmetric repect to the x axis

Part c

For this case f(-x) =-f(x) so then we can conclude that the function is odd

Part d

Intervals increasing:

[tex](-\infty,-3)U(2,\infty)[/tex]

Intervals decreasing:

[tex](-3,2)[/tex]

Part e

For this case the local maximum occurs at x=-3

(-3,5)

Part f

The local minimum for this case would be at x=2:

(2,-6)

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