SIGN IN

SIGN UP

ACCOUNT

DATA

NEXUS

A **function** is a mathematical rule that relates an input (usually denoted by \(x\)) to an output (denoted by \(f(x)\)). For each input value, there is exactly one output value.

The general form of a function is:

\[f(x) = \text{expression in terms of } x\]

The function:

\[f(x) = 2x + 3\]

will return the value of \(2x + 3\) for any value of \(x\)

To evaluate a function, substitute a specific value of \(x\) into the function.

\(f(x)=2x+3\text{, find }f(4)\)

\[f(4) = 2(4) + 3 = 8 + 3 = 11\]

The domain is the set of all possible input values (values of \(x\)) for which the function is defined.

The range is the set of all possible output values (values of \(f(x)\))

For \(f(x) = \sqrt{x}\), the domain is \(x \geq 0\) because square roots are only defined for non-negative values. The range is also \(f(x) \geq 0\)

In mathematics, the **roots** of a function are the values of the variable that make the function equal to zero. In other words, if \(f(x)\) is a function, the roots are the solutions to the equation:

\[f(x) = 0\]

Roots are also known as **x-intercepts** of the function, as they represent the points where the graph of the function intersects the x-axis.

Ultimate members get access to four additional questions with full video explanations.