Mathematics: Which statement describes the graph of this polynomial function? f(x)= x5 - 6x4+9x3 the graph crosses the x-axis at x = 0 and touches the x-axis at x = 3. the graph touches the x-axis at x = 0 and crosses the x-axis at x = 3. the graph crosses the x-axis at x = 0 and touches the x-axis at x = -3 o the graph touches the x-axis at x = 0 and crosses the x-axis at x = -3.

Domain is 8 range is 2 Step-by-step explanation:And if it passes the vehicle line test it is a function...

Which statement describes the graph of this polynomial

Maddenmobile7625

16.06.2020

The graph crosses the x-axis at x=0 and touches the x-axis at x=3.

Step-by-step explanation:

f(x) = $x^{5}-6x^{4}+9x^{3}$

Step 1:

We have to find the roots of the equation f(x)=0 to get the points where it touches x-axis.

$x^{5}-6x^{4}+9x^{3}=0\\x^{3}(x^{2}-6x+9)=0\\x^{3}(x-3)^{2}=0$

∴Roots are 0 and 3.

Step 2:

We have to find whether it crosses or touches the x-axis at points (0,0) and (3,0).

Simplied form of f(x) = $x^{3}(x-3)^{2}$

If we substitute a point between x=0 and x=3 we get f(x) to be positive.

If we substitute a point less than x=0 we get f(x) to be negative.

f(x) changes sign around x=0

Hence f(x) crosses the x-axis at x=0.

If we substitute a point greater than x=3 we get f(x) to be positive.

f(x) does not change its sign around x=3.

Hence f(x) touches the x-axis at x=3.

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