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$% .