NAME _____________________________________________ DATE__________________________ PERIOD ______ PAGE _____
1-8 Notes: Interpreting Graphs of Functions
I.
Intercepts & Symmetry
-
The _______________________ of a graph are points where the
graph intersects an axis.
-
The _______________________ is the point on the graph intersects
the y-axis
-
The _______________________ point at which a graph
intersects the x-axis.
-
A graph has _______________ ________________________ in a
line if each half of the graph on either side of the line matches exactly
Linear Graphs
Non Linear
Example: The graph shows a function that approximates the shape of
the Gateway Arch, where x is the distance from the center point in feet
and y is the height in feet.
A. Identify the function as linear or nonlinear.
B. Then estimate and interpret the intercepts,
and describe and interpret any symmetry.
x-intercept:
y-intercept:
symmetry:
II.
Interpret Extrema and End Behavior
A graph is positive if ____________________________________________________________________________.
A graph is negative if ____________________________________________________________________________.
A graph is increasing if ____________________________________________________________________________.
A graph is decreasing if ____________________________________________________________________________.
Relative Extrema:
- Relative Maximum:
- Relative Minimum:
End Behavior describes what is happening when _________________________________________________________
Example
The outbreak of the H1N1 virus can be modeled by
the function graphed at the right. Estimate and interpret
where the function is positive, negative, increasing, and
decreasing, the x-coordinates of any relative extrema, and
the end behavior of the graph.
Positive:
Negative:
Increasing:
Decreasing:
Relative Maximum:
Relative Minimum:
End Behavior:
Examples: Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph
and any symmetry. Estimate and interpret where the function is positive, negative, increasing, and decreasing, the x–
coordinate of any relative extrema, and the end behavior of the graph.
1.
2.
3.
a) Linear or nonlinear?
a) Linear or nonlinear?
b) x-intercept:
b) x-intercept:
c) y-intercept:
c) y-intercept:
d) symmetry?
d) symmetry?
e) Positive:
e) Positive:
f)
f)
Negative:
Negative:
g) Increasing:
g) Increasing:
h) Decreasing:
h) Decreasing:
i)
Relative maximum:
i)
Relative maximum:
j)
Relative minimum:
j)
Relative minimum:
k) End behavior:
k) End behavior:
a) Linear or nonlinear?
b) x-intercept:
c) y-intercept:
d) symmetry?
e) Positive:
f)
Negative:
g) Increasing:
h) Decreasing:
i)
Relative maximum:
j)
Relative minimum:
k) End behavior: