# Sign of a function

The sign of a function, that is, whether the values of the function are negative or positive.

The standard function f (x) = 3 is always 3, that is, positive. The function f (x) = - 2 is always -2, that is, negative.

The function f (x) = x has negative values when x < 0 and positive values when x > 0. The function changes the sign at its zero point, which is x = 0.

Example 1

When are the values of the function f(x) = 2x - 6 negative?

Solution

Let's form an inequality and solve it The values of the function are negative, when x < 3 We can see the same from the graph f(x) < 0, when x < 3

Example 2

When are the values of the function f(x) negative? The zeros of the function are x = 1 or x = 2. The graph of a function is an upward opening parabola and negative it is between its zeros. The function f (x) < 0 when 1 < x < 2 Example 3

When are the values of the function g(x) positive? Solution

The function g has no zeros because its discriminant is negative, The graph of the function g is a downward-opening parabola, so its values are only negative. The function g(x) does not have positive values for any value of x.

Turn on the subtitles if needed