Zeros of Functions

Front

What is a zero of a function?

Back

A zero of a function is a value of x that makes the function equal to zero. It is also known as a root of the function.

Front

How do you find the zeros of a linear function?

Back

To find the zeros of a linear function, set the function equal to zero and solve for x.

Front

What is the zero of the function t(x) = 3x + 6?

Back

The zero is x = -2.

Front

What does it mean if a function has no zeros?

Back

If a function has no zeros, it means that there are no values of x for which the function equals zero.

Front

What is the relationship between the zeros of a function and its graph?

Back

The zeros of a function correspond to the x-intercepts of its graph, where the graph crosses the x-axis.

Front

How can you verify if a number is a zero of a function?

Back

To verify if a number is a zero, substitute it into the function. If the result is zero, then it is a zero of the function.

Front

What is the zero of the function t(x) = 24 - 48x?

Back

The zero is x = 1/2.

Front

What are the zeros of the quadratic function f(x) = x^2 - 5x + 6?

Back

The zeros are x = 2 and x = 3.

Front

What is the significance of finding the zeros of a function in real-world applications?

Back

Finding the zeros of a function can help determine critical points, such as break-even points in business or points of intersection in physics.

Front

What is the zero of the function f(x) = x^2 + 4?

Back

There are no real zeros, as the function does not cross the x-axis.