4. Polynomial Functions

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

For each polynomial function, identify its graph from choices A–F.

$\text{ƒ}\left(x\right)=(x-2)(x-5)$

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. f(x)=11x⁴−6x²+x+3

Use a graphing calculator to find the coordinates of the turning points of the graph of each polynomial function in the given domain interval. Give answers to the nearest hundredth. ƒ(x)=2x³-5x²-x+1; [-1, 0]

Show that the real zeros of each polynomial function satisfy the given conditions. ƒ(x)=x⁴+x³-x²+3; no real zero less than -2

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

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

$\text{ƒ}\left(x\right)=x^3+x^2-36x-36$

Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. ƒ(x)=2x⁴

Graph the following on the same coordinate system.

(a) y = (x - 2)²

(b) y = (x + 1)²

(c) y = (x + 3)²

(d) How do these graphs differ from the graph of y = x²?

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

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

Find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. $f\left(x\right)=x^3+7x^2-4x-28$

Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. ƒ(x)=2x⁴-4x²+4x-8; 1 and 2

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

Use a graphing calculator to find the coordinates of the turning points of the graph of each polynomial function in the given domain interval. Give answers to the nearest hundredth. ƒ(x)=x³+4x²-8x-8; [-3.8, -3]