Unit 6, Lesson 5
Some Functions Have Symmetry
Algebra 2
Practice
Problem 1
Classify each function as odd, even, or neither.
A graph of function a on a coordinate plane. X axis from negative 10 to 8, by 2’s. Y axis from negative 10 to 8, by 2’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 5 comma 5, continues downward reaching minimum near negative 3 comma negative 9. It then curves up crossing the x axis at around negative 1, touches 0 comma 1 and then curves back down crossing the x axis at around 1 until it reaches 3 comma negative 9. It then curves back upward and to the right, crosses the x axis around 4, and continues to move upward and to the right, ending in the first quadrant.
A graph of function b on a coordinate plane. X axis from negative 10 to 8, by 2’s. Y axis from negative 10 to 8, by 2’s. From left to right, the function begins in the second quadrant around negative 10 comma 4, moves downward and to the right, crossing the x axis at approximately 9 point 5, continues down and to the right reaching a minimum at around negative 8 comma negative 8. Moves upward and to the right crossing the x axis at around negative 6 then reaches a maximum at around negative 5 comma 8. Then moves down and to the right crossing the x axis around negative 3 reaching a minimum around negative 1 comma negative 8. Then it moves upward and to the right crossing the x axis at around 0 and reaching a maximum around 2 comma 8. It moves downward crossing the x axis around 3 reaching a minimum around 5 comma negative 8. It moves upward and to the right crossing the x axis around 6 reaching a maximum around 8 comma 8. Finally it moves downward and to the right ending in the the fourth quadrant.
Graph of function c. X axis from negative 10 to 8, by 2’s. Y axis from negative 10 to 8, by 2’s.Vertical asymptotes at negative 2 and 2. From left to right, function starts around negative 10 comma negative 10 moves upward and to the right to about negative 3 comma negative 4 then moves down close to the vertical asymptote at negative 2. Part 2 of the function begins around negative 2 comma 10 crosses the y axis at 1 then moves downward and to the right crossing the x axis around 1 point 5 then moves downward and to the right close to the vertical asymptote at 2. The third part of the function begins around 2 comma 10 moves downward and to the right to about 3 comma 6 then moves upward and to the right.
A graph of function d on a coordinate plane. X axis from negative 10 to 8, by 2’s. Y axis from negative 10 to 8, by 2’s. From left to right, the function begins in the third quadrant around negative 10 comma negative 2, moves upward and to the right, crossing the x axis at approximately 0, continues upward and to the right ending in the first quadrant around 10 comma 2.