# Glossary for Lesson 19: Behavior of Functions

### Absolute Maximum

An *absolute maximum*, also known as a *global maximum*, is the value of a function at the highest point that the curve ever reaches. The absolute maximum is thus the largest range value of the function.

### Relative Maximum

A *relative maximum*, also known as a *local maximum*, is the value of a function at its highest point in some interval.

### Absolute Minimum

An *absolute minimum*, also known as a *global minimum*, is the value of a function at the lowest point that the curve ever reaches. The absolute minimum is thus the smallest range value of the function.

### Relative Minimum

A *relative minimum*, also known as a *local minimum*, is the value of a function at its highest point in some interval.

### Even Function

A function that is symmetry with respect to the y-axis is an *even function*. In terms of the equation of the function, this will mean that for every value of x in the domain, f(-x)=f(x) .

### Odd Function

A function that is symmetry with respect to the origin is an *odd function*. In terms of the equation of the function, this will mean that for every value of x in the domain, f(-x)=-f(x) .

### Symmetry

An object is *symmetric* or has *symmetry* with respect to a certain transformation if the image of the object is no different after that transformation has been performed on it.

### Constant Function

A function is a *constant function* if it can be written in the form f(x)=c , where c is a constant.

### Linear Function

A function is a *linear function* if it can be written in the form f(x)=mx+b , where m and b are constants. The simplest linear function is f(x)=x .

### Quadratic Function

A function is a *quadratic function* if it can be written in the form f(x)=ax^2+bx+c , where a , b , and c are constants. The simplest quadratic function is f(x)=x^2 .

### Cubic Function

A function is a *cubic function* if it can be written in the form f(x)=ax^3+bx^2+cx+d , where a , b , c , and d are constants. The simplest cubic function is f(x)=x^3 .

### Absolute Value Function

A function is an *absolute value function* if it can be written in the form f(x)=a|x-h|+k% , where a , h , and k are constants. The simplest absolute value function is f(x)=|x| .</p>
<h3 id="square-root-function">Square Root Function</h3>
<p>A function is a <em>square root function</em> if it can be written in the form f(x)=a\sqrt{x-h}+k , where a , h , and k are constants. The simplest square root function is f(x)=\sqrt x$% .