Question

What are the zeros of the function shown in the graph?

The graph starts at the bottom left, continues up through the x axis at negative three to a maximum around y equals three, goes back down through the x axis at negative one to a minimum around y equals negative one, and goes back up through the x axis at one.


A. −1, 1, 2

B. −2, −1, 1

C. −3, −1, 1

D. −1, 1, 3

Answer 1

The zeroes of the function are -3 , -1 , 1 ⇒ 3rd answer

Explanation:

* Lets explain the meaning of the zeroes of the function

- The zeroes of the function are the values of x when f(x) = 0

- That means the coordinates of the intersection points between the

curve and the x-axis

- Ex: If the graph of f(x) intersects the x-axis at points (p , 0) , (q , 0) ,

(r , 0) then the zeroes of f(x) are p , q , r

* Lets solve the problem

- The graph starts at the bottom left

- It continues up through the x-axis at negative three

- That means it intersects the x-axis at point (-3 , 0)

∴ The first zero of the function is -3

- It goes to a maximum around y equals three

- It goes back down through the x-axis at negative one

- That means it intersects the x-axis again at point (-1 , 0)

∴ The second zero of the function is -1

- It goes to a minimum around y equals negative one

- It goes back up through the x-axis at one

- That means it intersects the x-axis again at point (1 , 0)

∴ The third zero of the function is 1

∴ The function has three zeroes -3 , -1 , 1

* The zeroes of the function are -3 , -1 , 1