Zero of a function
The zero of a function, also known as the root, is a value of the independent variable (usually denoted by x) for which the function evaluates to zero
The zero of a function, also known as the root, is a value of the independent variable (usually denoted by x) for which the function evaluates to zero. In simpler terms, it is the x-value at which the function intersects or touches the x-axis on a graph.
To find the zeros of a function algebraically, we set the function equal to zero and solve for the variable. For example, let’s consider the quadratic function f(x) = x^2 – 4. To find its zeros, we set f(x) = 0:
x^2 – 4 = 0
Applying the zero product property, we factor the equation:
(x – 2) (x + 2) = 0
Now we can use the zero product property again and set each factor equal to zero:
x – 2 = 0 or x + 2 = 0
This gives us two solutions:
x = 2 or x = -2
Therefore, the zeros of the function f(x) = x^2 – 4 are x = 2 and x = -2.
Graphically, the zeros of a function correspond to the x-intercepts or the points where the graph of the function intersects the x-axis.
More Answers:
[next_post_link]