Question

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

Answer 1

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»ANSWER«

(1) Write properties of function:

x intercept/zero:

`x_(1) = (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 = (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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