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Describing Key Features of a Graph of a Polynomial Function:
Explain how to sketch a graph of the function f(x) = x3 + 2x2 – 8x. Be sure to include end-behavior, zeroes, and intervals where the function is positive and negative.

Respuesta :

tramserran

End behavior:

The parent function is: f(x) = x³, which starts (from the left side) at -∞ and ends (on the right side) at +∞.

Zeroes:

f(x) = x³ + 2x² - 8x

0 = x³ + 2x² - 8x

0 = x(x² + 2x - 8)    

0 = x(x + 4)(x - 2)

0 = x         0 = x + 4         0 = x - 2

x = 0            x = -4              x = 2

Intervals:

Put the zeroes in order: -4, 0, 2

since f(x) is increasing from the left then the interval from -4 to 0 is positive and the interval from 0 to 2 is negative.

Graph:

see attachment



Ver imagen tramserran

Answer:

The degree of the function is odd and the leading coefficient is positive – so the function goes to negative infinity as x goes to negative infinity and to positive infinity as x goes to positive infinity.

The zeroes are –4, 0, and 2, all with multiplicity 1.

The function is negative from negative infinity to –4 and from 0 to 2.

The function is positive from –4 to 0 and from 2 to infinity.

Step-by-step explanation: