Here is a graph of for . Draw the graph for , and be prepared to explain your reasoning if:

1. is even

   

   A graph of function f on a coordinate plane. X axis from negative 4 to 4, by 1’s. Y axis from negative 4 to 4, by 1’s. From left to right, the function begins in the second quadrant, moves downward and to the right, crossing the x axis at approximately negative 4, continues downward reaching minimum at negative 3 point 4 comma negative 3 point 0. It then curves up crossing the x axis at negative 2 until it reaches negative 1 point 4 comma 0 point 4. It curves back down until it reaches about 0 point 5 comma 0.

2. is odd

   

   A graph of function f on a coordinate plane. X axis from negative 4 to 4, by 1’s. Y axis from negative 4 to 4, by 1’s. From left to right, the function begins in the second quadrant, moves downward and to the right, crossing the x axis at approximately negative 4, continues downward reaching minimum at negative 3 point 4 comma negative 3 point 0. It then curves up crossing the x axis at negative 2 until it reaches negative 1 point 4 comma 0 point 4. It curves back down until it reaches about 0 point 5 comma 0.

3. is neither even nor odd

   

   A graph of function f on a coordinate plane. X axis from negative 4 to 4, by 1’s. Y axis from negative 4 to 4, by 1’s. From left to right, the function begins in the second quadrant, moves downward and to the right, crossing the x axis at approximately negative 4, continues downward reaching minimum at negative 3 point 4 comma negative 3 point 0. It then curves up crossing the x axis at negative 2 until it reaches negative 1 point 4 comma 0 point 4. It curves back down until it reaches about 0 point 5 comma 0.

Take turns with your partner to decide if the function is even, odd, or neither. If it’s your turn, explain to your partner how you decided. If it’s your partner’s turn, listen carefully to their reasons and decide if you agree. If you disagree, discuss your thinking and work to reach an agreement.