# SOLUTION: Given the function f(x)=x(x-2)^2(x-4) I. find x and y intercept II.Determine whether the graph crosses or touches the x-axis at each intercept III. Graph the function

Algebra ->  Algebra  -> Functions -> SOLUTION: Given the function f(x)=x(x-2)^2(x-4) I. find x and y intercept II.Determine whether the graph crosses or touches the x-axis at each intercept III. Graph the function      Log On

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 Algebra: Functions, Domain, NOT graphing Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Functions Question 550135: Given the function f(x)=x(x-2)^2(x-4) I. find x and y intercept II.Determine whether the graph crosses or touches the x-axis at each intercept III. Graph the functionAnswer by lwsshak3(6505)   (Show Source): You can put this solution on YOUR website!Given the function f(x)=x(x-2)^2(x-4) I. find x and y intercept II.Determine whether the graph crosses or touches the x-axis at each intercept III. Graph the function ** I. x-intercept: set y=0, then solve for x x(x-2)^2(x-4=0 x-intercepts=0,2(mult. 2), and 4 .. y-intercept set x=0, then solve for y y-intercept=x(x-2)(x-2)(x-4) .. II. Number line: <....+....0....-....2...-.....4...+.....> For x>4, f>0 Moving to the left, the sign of each interval switches each time we go thru a zero of odd multiplicity like 1, 3, 5, etc. The sign of each in interval does not change if we go thru a zero of even multiplicity like 2, 4, 6, etc. Accordingly, the graph crosses the x-axis at x= 0 and 4, but at x=2, only touches but does not cross the x-axis. .. III.See graph below as a visual check on the above: ..