1.8 Interpreting Graphs of Functions
Intercepts
x-intercept
y-intercept
Mrs. Algebra's Bank Account
Amount ($)
5000
2
4
6
8
10
12
14
Month
Explain what the x-intercept
and the y-intercept represent.
Line Symmetry
Positive & Negative Functions
A function is positive where
its graph lies above the x-axis
and negative where its
graph lies below the x-axis.
Increasing & Decreasing Functions
A function is increasing where the graph goes up
and decreasing where the graph goes down.
(left to right !)
d
sin
a
e
r
dec
g
inc
rea
sin
g
a si n
e
r
ec
g
Extrema:
the locations of relatively high or low values
relative maximum
relative minimum
End Behavior
As x decreases, y increases
As x increases, y decreases
End behavior that approaches zero
Linear or Nonlinear?
Estimate the intercepts
Any symmetry?
Identify where the function is
positive & negative
Identify where the function is
increasing & decreasing
Identify x-coordinate of any
relative extrema
Identify the end behavior
Sketch a graph of a function with the
following characteristics:
The graph is linear
with an y-intercept at 5.
The graph is positive
for x > -3, and the
graph is negative
for x < -3
Sketch a graph of a function with the
following characteristics:
A non-linear graph has
x-intercepts at -4 and 2
and y-intercept at 6.
The graph has a relative
maximum of 7 at x = -1.
The graph is decreasing
for x > -1 and increasing for x < -1