4. Polynomial Functions

Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4.

$\text{ƒ}\left(x\right)=-3x^4-5x^3+2x^2$

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = x² - 4x + 3

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=2x³(x²-4)(x-1)

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=2x³-5x²-x+6

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = -2x² - 8x - 7

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=2x⁴+x³-6x²-7x-2

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = -3x² + 18x + 1

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=3x⁴-7x³-6x²+12x+8

If the given term is the dominating term of a polynomial function, what can we conclude about each of the following features of the graph of the function? (a) domain (b) range (c) end behavior (d) number of zeros (e) number of turning points 10x⁷

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=x4+3x³-3x²-11x-6

If the given term is the dominating term of a polynomial function, what can we conclude about each of the following features of the graph of the function? (a) domain (b) range (c) end behavior (d) number of zeros (e) number of turning points -9x⁶

Graph each polynomial function. ƒ(x)=(x-2)²(x+3)

Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. ƒ(x)=3x²-x-4; 1 and 2

Graph each polynomial function. ƒ(x)=2x³+x²-x

Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. ƒ(x)=-2x³+5x²+5x-7; 0 and 1