Graph polynomial functions: zeros, multiplicity and end behavior, and match equations to graphs

Grade 11 Math Worksheet

Circle the best answer.

1. 1.

   Esme finds a graph on a math club poster. Which equation matches it?

   • (x + 3)(x − 1)(x − 4)
   • (x + 3)(x − 1)²(x − 4)
   • (x − 3)(x + 1)²(x + 4)
   • -(x + 3)(x − 1)²(x − 4)
2. 2.

   Jun's robot prints a graph and its features. Which equation matches it?

   • -(x − 4)²(x + 2)
   • -(x + 4)(x − 2)
   • -(x + 4)²(x − 2)
   • (x + 4)²(x − 2)
3. 3.

   Kira sketches a graph from a table of values. Which equation matches it?

   • x(x + 5)(x − 2)²
   • -x(x − 5)(x + 2)²
   • -x(x + 5)(x − 2)²
   • -x(x + 5)(x − 2)
4. 4.

   Luz finds a graph on a grid map. Which equation matches it?

   • (x − 2)(x + 1)(x + 5)
   • -(x − 2)²(x + 1)(x + 5)
   • (x + 2)²(x − 1)(x − 5)
   • (x − 2)²(x + 1)(x + 5)
5. 5.

   Milo studies p(x) = -(x − 1)²(x + 3)³ on graph paper. What does the graph do far to the left and far to the right?

   • Falls on the left and rises on the right.
   • Rises on both sides.
   • Falls on both sides.
   • Rises on the left and falls on the right.
6. 6.

   Noah's robot graphs p(x) = 2x³(x + 6)⁴. What does the graph do far to the left and far to the right?

   • Rises on the left and falls on the right.
   • Falls on both sides.
   • Rises on both sides.
   • Falls on the left and rises on the right.
7. 7.

   Ren sketches p(x) = 4(x + 2)²(x − 5). What does the graph do far to the left and far to the right?

   • Rises on the left and falls on the right.
   • Rises on both sides.
   • Falls on both sides.
   • Falls on the left and rises on the right.
8. 8.

   Tala plans p(x) = -x²(x − 7)³(x + 1) on a grid map. What does the graph do far to the left and far to the right?

   • Rises on both sides.
   • Rises on the left and falls on the right.
   • Falls on the left and rises on the right.
   • Falls on both sides.
9. 9.

   Bo's robot graphs p(x) = -x³ + 27x. What is the range of p?

   • -3 ≤ y ≤ 3
   • -54 ≤ y ≤ 54
   • y ≤ 54
   • All real numbers
10. 10.

    Esme graphs p(x) = x⁴ − 8x² + 3 from a table. What is the range of p?

    • y ≤ -13
    • y ≥ -13
    • All real numbers
    • y ≥ 2