Blake Franklin
04/05/2024 · Junior High School

For the given polynomial function, complete the following. (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the \( x \)-axis at each \( x \)-intercept. (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of \( f \) resembles for large values of \( |x| \). \( f(x)=(x-6)^{3}(x+3)^{2} \) The multiplicity of the larger zero is 3 . (Type a whole number.) The multiplicity of the smaller zero is 2 . (Type a whole number.) (b) The graph touches the \( x \). \( x_{2} \) axis at the larger \( x \)-intercept. The graph crosses the \( x \)-axis at the smaller \( x \)-intercept. (c) The maximum number of turning points on the graph is 3 . (d) Type the power function that the graph of \( f \) resembles for large values of \( |x| \). \( y=\square \)

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(a) Real zeros: \( x = 6 \) (multiplicity 3), \( x = -3 \) (multiplicity 2). (b) Graph touches \( x \)-axis at \( x = 6 \), crosses at \( x = -3 \). (c) Maximum turning points: 3. (d) End behavior: \( y = x^{3} \).

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