**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*.

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