The features of a function graph can show us many aspects of the relationship represented by the function. Let's take a look at the more popular graphical features. Be sure to pay attention to the
Intercepts are the locations (points) where the graph crosses (or touches)
When looking for sections of a graph that are increasing or decreasing,
By definition: A function is strictly decreasing on an interval, if when x1 < x2, If the function notation is bothering you, this definition can also be thought of as stating x1 < x2 implies y1 > y2. Example: The graph shown above is decreasing from the point (3,4) to the point (5,-5), described as decreasing when 3 < x < 5.
By definition: A function is constant, if for any x1 and x2 in the interval, f (x1) = f (x2). Example: The graph shown above is constant from the point (-2,1) to the point (1,1), described as constant when -2 < x < 1. The y-values of all points in this interval are "one".
For maximum/minimum, symmetry, and end-behavior, see More Function Features. NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation Topical Outline | Algebra 1 Outline | MathBitsNotebook.com | MathBits' Teacher Resources Terms of Use Contact Person: Donna Roberts | |||||||||||||||||||||||||||||
To find the 
FAQs
What are the features of graphs of functions? ›
Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
What is the Y value of a function that is positive? ›A function is positive when the y values are greater than 0 and negative when the y values are less than zero. Here's the graph of a function: This graph is positive when x is less than 2 and negative when x is greater than 2.
What are the key features of functions positive and negative? ›The positive regions of a function are those intervals where the function is above the x-axis. It is where the y-values are positive (not zero). The negative regions of a function are those intervals where the function is below the x-axis. It is where the y-values are negative (not zero).
What are the characteristics of functions in Algebra 2? ›A function can be described as either increasing, decreasing or constant. Some functions will be increasing, decreasing or constant only in specific intervals of the domain.
What are the 4 main features of a graph? ›- y-axis is the vertical axis.
- x-axis is the horizontal axis.
- Origin is the point where both the x-axis and y-axis are zero and intersect.
- Title – relating to the information being displayed on the graph.
- Domain, Range, Max, Min, Zero,
- Y-Intercept, Interval of Increase,
- and Interval of Decrease.
A positive y-intercept means the line crosses the y-axis above the origin, while a negative y-intercept means that the line crosses below the origin. The slope intercept form of a linear equation is written as , where m is the slope and b is the value of y at the y-intercept.
How do you tell if a function is positive or negative from equation? ›The sign of a function is a description indicating whether the function is positive, negative, or zero. For the function 𝑓 ( 𝑥 ) on an interval 𝐼 , the sign is positive if 𝑓 ( 𝑥 ) > 0 for all 𝑥 in 𝐼 , the sign is negative if 𝑓 ( 𝑥 ) < 0 for all 𝑥 in 𝐼 .
How to find y for a function? ›To find the y -value: Insert the x -value you have been given into the function, and calculate the value. To find the x -value: Set f ( x ) equal to the y -value you've been given, and solve the equation for x .
Which functions are positive? ›- All trig functions (sin, cos, tan, sec, csc, cot) are positive in the first quadrant.
- Sine is positive in the second quadrant.
- Tangent is positive in the third quadrant.
- Cosine is positive in the fourth quadrant.
What are the features of positive real function? ›
There are some important properties of a positive real function, which are listed below: The numerator and denominator of F(v) must be Hurwitz polynomials. The degree of the numerator of F(v) must not be more than the degree of the denominator by more than 1. In other words, (N-n) must be lesser than or equal to one.
What is end behavior on a graph? ›End behavior: The end behavior of a polynomial function (a function containing a sum of terms of the form a x n , where is a positive whole number and is a constant real number) describes what the graph of the function looks like as approaches positive or negative infinity .
Is price a function of item? ›Each item on the menu has only one price, so the price is a function of the item. Two items on the menu have the same price. If we consider the prices to be the input values and the items to be the output, then the same input value could have more than one output associated with it.
What are the key features of a function graph? ›Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
What are graph features? ›A feature graph is a finite, rooted, connected and directed graph for which the following properties must hold : Edges are labeled with features. For every node, the labels of the out-coming edges must be pairwise distinct. Every inner node must be a variable and. every leaf node must be either a constant or a variable ...
What are the 4 types of graph functions? ›There are eight different types of functions that are commonly used, therefore eight different types of graphs of functions. These types of function graphs are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal.
What are the key features of the graphs of polynomial functions? ›The graph of a polynomial function will touch the x-axis at zeros with even multiplicities. The graph will cross the x-axis at zeros with odd multiplicities. The sum of the multiplicities is no greater than the degree of the polynomial function.
What are the key features of the graph of an exponential function? ›The main properties of exponential functions are a y-intercept, a horizontal asymptote, a domain (x-values at which the function exists) of all real numbers, and a constant growth factor, b.