4. Polynomial Functions

Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. See Example 5. ƒ(x)=x^4-4x^3-x+3; 0.5 and 1

For each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)^2(x-5)

For each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)^2(x-5)

For each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)^2(x-5)^2

For each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)(x-5)

Show that the real zeros of each polynomial function satisfy the given conditions. See Example 6. ƒ(x)=x^4-x^3+3x^2-8x+8; no real zero greater than 2

Show that the real zeros of each polynomial function satisfy the given conditions. See Example 6. ƒ(x)=2x^5-x^4+2x^3-2x^2+4x-4; no real zero greater than 1

For each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)^2(x-5)^2

Show that the real zeros of each polynomial function satisfy the given conditions. See Example 6. ƒ(x)=x^4+x^3-x^2+3; no real zero less than -2

Show that the real zeros of each polynomial function satisfy the given conditions. See Example 6. ƒ(x)=x^5+2x^3-2x^2+5x+5; no real zero less than -1

Show that the real zeros of each polynomial function satisfy the given conditions. See Example 6. ƒ(x)=3x^4+2x^3-4x^2+x-1; no real zero greater than 1

Show that the real zeros of each polynomial function satisfy the given conditions. See Example 6. ƒ(x)=3x^4+2x^3-4x^2+x-1; no real zero less than -2

Show that the real zeros of each polynomial function satisfy the given conditions. See Example 6. ƒ(x)=x^5-3x^3+x+2; no real zero greater than 2

Show that the real zeros of each polynomial function satisfy the given conditions. See Example 6. ƒ(x)=x^5-3x^3+x+2; no real zero less than -3

Find a polynomial function f of least degree having the graph shown. (Hint: See the NOTE following Example 4.)