Finding the Zeros of Functions

Front

What is a zero of a function?

Back

A zero of a function is a value of x for which the function f(x) = 0.

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 an x-intercept?

Back

An x-intercept is a point where the graph of a function crosses the x-axis, meaning the output (y-value) is zero.

Front

If f(x) = x^2 - 4, what are the zeros of the function?

Back

The zeros are x = -2 and x = 2.

Front

What does it mean if a function has multiple zeros?

Back

It means that the function crosses the x-axis at more than one point.

Front

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

Back

Substitute the number into the function; if the result is zero, then it is a zero of the function.

Front

What is the relationship between zeros and factors of a polynomial?

Back

If x = a is a zero of a polynomial, then (x - a) is a factor of that polynomial.

Front

Find the zeros of the function f(x) = x^2 - 5x + 6.

Back

The zeros are x = 2 and x = 3.

Front

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

Back

Zeros can represent solutions to equations, points of equilibrium, or break-even points in various contexts.

Front

If a function has a zero at x = 1, what does this indicate about the function's graph?

Back

The graph of the function will cross the x-axis at the point (1, 0).