Knock out the false claims about zeros

Exercise and reference answers

Questions

1. Question

   Three of these statements about a zero of even multiplicity are false.

   Choices

   1. Item

      The graph touches the axis and turns back

      Correct

      Yes

   2. Explanation

      Crossing marks odd multiplicity, not even.

      Item

      The graph always crosses the axis there

   3. Explanation

      It is an x-intercept, so it is real.

      Item

      The zero must be an imaginary number

   4. Explanation

      It adds its own multiplicity, which is 2 or more.

      Item

      The zero raises the degree by exactly one

2. Question

   Three of these statements about a degree 5 polynomial are false.

   Choices

   1. Item

      It has at most four turning points

      Correct

      Yes

   2. Explanation

      The ceiling on x-intercepts is the degree, so five.

      Item

      It has at most six x-intercepts

   3. Explanation

      Polynomial graphs are smooth everywhere.

      Item

      Its graph can have a sharp corner

   4. Explanation

      Polynomial graphs are continuous everywhere.

      Item

      Its graph can break into two pieces

Instructions

Tap the three false claims in each round to knock them out and leave the true one standing.

Explanation