Exercises: Graph Polynomial Functions, Identifying Zeros and Showing End Behavior

Work through each section in order. Show your work where indicated.

Grade 9·20 problems·~30 min·Common Core Math - HS Functions·standard·hsf-if-c-7c

Work through problems with immediate feedback

Recall / Warm-Up

What are the zeros of $f(x) = (x - 3)(x + 5)$ ?

$x = 3$ and $x = -5$

$x = -3$ and $x = 5$

$x = 3$ and $x = 5$

$x = -3$ and $x = -5$

Factor $f(x) = x^3 - 9x$ . What are the zeros?

$x = 0$ only

$x = 3$ and $x = -3$

$x = 0$ , $x = 3$ , and $x = -3$

$x = 9$ and $x = -9$

Which of the following is TRUE about polynomial functions?

Polynomial graphs can have vertical asymptotes where the function is undefined.

Polynomial graphs are smooth, continuous curves defined for all real numbers.

A polynomial of degree $n$ has exactly $n$ turning points.

The end behavior of a polynomial depends on its middle terms.

What are the zeros of $g(x) = (x + 1)(x - 2)(2x - 6)$ ?

$x = -1$ , $x = 2$ , $x = 6$

$x = 1$ , $x = -2$ , $x = 3$

$x = -1$ , $x = 2$ , $x = 3$

$x = -1$ , $x = 2$ , $x = -3$

How many zeros does $f(x) = x(x^2 + 1)(x - 4)$ have (counting real zeros only)?

What is the degree of $f(x) = (x + 3)^2(x - 1)(x - 4)^3$ ?

What is the end behavior of $f(x) = -3x^4 + 7x^2 - x + 100$ ?

Rises to the left, rises to the right.

Falls to the left, falls to the right.

Falls to the left, rises to the right.

Rises to the left, falls to the right.

What is the end behavior of $f(x) = 2x^5 - 10x^3 + x$ ?

Falls to the left, rises to the right.

Rises to the left, falls to the right.

Falls on both ends.

Rises on both ends.

You're viewing 2 of 6 sections.

Create a free account to continue the full exercise set and save your progress.

0 of 8 answered

Answer all problems to submit.