Functions 3.8.

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Presentation transcript:

Functions 3.8

Functions A function is a rule that takes an input value and assigns a particular output value to it. For a rule to define a function, it is necessary that each input value is assigned one and only one output value. The set of input values for a function is called the domain of the function. The set of output values for a function is called the range of the function.

Functions A function is a rule that takes an input value and assigns a particular output value to it. For a rule to define a function, it is necessary that each input value is assigned one and only one output value. The set of input values for a function is called the domain of the function. The set of output values for a function is called the range of the function.

Functions Is a relation whose input value is a student at your college and whose output is the month the student was born in? Yes, because each student has only one birth month.

The Vertical Line Test If a vertical line can be drawn that intersects a graph at more than one point, then the graph does not represent a function.

The Vertical Line Test Not A Function

Function Notation Function notation is a way to present the formula for the output value of a function for the input x.

Function Notation Function name: Input variable: Formula for output:

Evaluating Functions To evaluate a function for a particular value of the variable, we substitute that value for the variable in the function’s formula, and then we simplify the resulting expression.

Evaluating Functions For find

Interpreting Graphs The domain of a function can be read from left to right along the x-axis on a graph. The range of a function can be read vertically from the bottom of the graph to the top along the y-axis. An x-intercept is a point where a graph intersects the x-axis. The y-coordinate of an x-intercept is 0. A y-intercept is a point where a graph intersects the y-axis. The x-coordinate of a y-intercept is 0.

Interpreting Graphs Domain: x-intercept: y-intercept: Range: