
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.
Intercepts are the locations (points) where the graph crosses (or touches) either the xaxis or yaxis.
• To find the yintercept, look where x = 0.
Remember: the
yintercept will have an xcoordinate of 0.
y = 2x + 2
y = 2(0) + 2; y = 2 yintercept: (0,2)
(You can also read the yintercept, b, from the function equation
if it is
in y = mx + b form.)
• To find the xintercept, look where y = 0.
Remember: the xintercept will have a ycoordinate of 0.
y = 2x + 2
0 = 2x + 2; 2x = 2; x = 1 xintercept: (1,0)




yvalues positive
or
yvalues negative 

• The positive regions of a function are those intervals where the function is above the xaxis.
It is where the yvalues are positive (not zero).
• The negative regions of a function are those intervals where the function is below the xaxis.
It is where the yvalues are negative (not zero).
• yvalues that are on the xaxis are neither positive nor negative. The xaxis is where y = 0. 
Some functions are positive over their entire domain
(All yvalues above the xaxis.)
positive: ∞ < x < +∞
or "all Reals", or (∞,+∞) 
Some functions are negative over their entire domain.
(All yvalues below the xaxis.)
negative: ∞ < x < +∞
or "all Reals", or (∞,+∞) 
Some functions have both positive and negative regions.
(yvalues above and below xaxis)
positive:
x > 0 or (0,+∞)
negative: x < 0 or (∞,0)
(do not include zero) 

Secret to Finding the Intervals!
The secret to correctly stating the intervals where a function is positive or negative is to remember that the intervals ALWAYS pertain to the locations of the xvalues. Think of reading the graph from left to right along the xaxis.
Do NOT read numbers off the yaxis for the intervals. Stay on the xaxis!

When looking for sections of a graph that are increasing or decreasing, be sure to look at (or "read") the graph from left to right.
• Increasing: A function is increasing, if as x increases (reading from left to right), y also increases .
In plain English, as you look at the graph, from left to right, the graph goes uphill. The graph has a positive slope.
Example: The function (graph) at the right is increasing from the point (5,3) to the point (2,1), which is described as increasing when 5 < x < 2 .
It also increases from the point (1,1) to the point (3,4), described as increasing when 1 < x < 3.


• Decreasing: A function is decreasing, if as x increases (reading from left to right), y decreases. In plain English, as you look at the graph, from left to right, the graph goes downhill. The graph has a negative slope.
Example: The graph shown above is decreasing from the point (3,4) to the point (5,5), described as decreasing when 3 < x < 5.
• Constant: A function is constant, if as x increases (reading from left to right), y stays the same. In plain English, as you look at the graph, from left to right, the graph goes flat (horizontal). The graph has a slope of zero.
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 yvalues of all points in this interval are "one".

Intervals of increasing, decreasing or constant ALWAYS pertain to xvalues.
Do NOT read numbers off the yaxis.
Stay on the xaxis for these intervals!

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