Identify and explain the zeros of the function. Show how to solve for f(x)=0 to find the x-intercepts.
To identify and explain the zeros of a function, we need to solve for f(x)=0. The solutions to this equation are also known as the x-intercepts or zeros of the function.
To solve for f(x)=0, follow these steps:
1. Write down the given function. Let's say our function is f(x).
2. Set the function equal to zero: f(x) = 0.
3. Solve the equation to find the values of x that make the function equal to zero. This can be done using various methods such as factoring, the quadratic formula, completing the square, or graphing the function.
4. Once you have determined the values of x that satisfy f(x) = 0, these are the zeros or x-intercepts of the function.
Explanation Example:
Let's consider the function f(x) = x^2 - 9.
To solve for f(x) = 0, we set the function equal to zero:
x^2 - 9 = 0.
Now, we can factor the equation:
(x - 3)(x + 3) = 0.
To solve for x, we set each factor equal to zero:
x - 3 = 0 or x + 3 = 0.
Solving each equation separately, we find:
x = 3 or x = -3.
Therefore, the zeros or x-intercepts of the function f(x) = x^2 - 9 are x = 3 and x = -3.