Question

The function after synthetic division f(x) = 4x3 + 3x2 − 16x − 12

Answer 1

Answer:

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»ANSWER«

(1) Write properties of function:

x intercept/zero:

$x_{1} = \frac{3}{4}$

y intercept:

$y = - 12$

domain:

$( - \infty \: \infty )$

type of function: cubic fraction

standard form:

$f(x) = 4 {x}^{3} - 3 {x}^{2} + 16x - 12$

factorize form:

$f(x) = (4x - 3)( {x}^{2} + 4)$

even/odd/neither: neither

bounce/cross x axis:

$x = \frac{3}{4} \: across$

increasing interval:

$( - \infty \: \infty )$

decreasing interval: no

number of positive real zeros: 1

number of possible turning point: 2

order/degree: 3

leading term:

$4x ^{3}$

leading coefficent: 4

constant term: -12

end behavior:

$as \: x \: → \infty f(x) → \infty \: as \: x → - \infty f(x) → - \infty$

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