Determining the Key Features of Function Graphs. The Key Features of Function Graphs - Preview ...
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The Key Features of Function Graphs - Preview Domain and Range x-intercepts and y-intercepts Intervals of increasing, decreasing, and
constant behavior Parent Equations Maxima and Minima
Domain Domain is the set of all possible input or
x-values To find the domain of the graph we look
at the x-axis of the graph
Identifying the Domain1. Start at the far left of the graph.2. Move along the x-axis until you find the
lowest possible x-value of the graph. This is your lower bound. Note if you have a open circle or a closed circle.
3. Keep moving along the x-axis until you find your highest possible x-value of the graph. This is your upper bound. Note if you have a open circle or a closed circle.
Your Turn: Complete problems 3, 7, and find the
domain of 9 and 10 on pg. 160 from the Xeroxed sheets
3. 7.
9. 10.
Range The set of all possible output or y-
values To find the range of the graph we look
at the y-axis of the graph We also use open and closed circles for
the range
***Identifying the Range1. Start at the bottom of the graph.2. Move along the y-axis until you find the
lowest possible y-value of the graph. This is your lower bound. Note if you have a open circle or a closed circle.
3. Keep moving along the y-axis until you find your highest possible y-value of the graph. This is your upper bound. Note if you have a open circle or a closed circle.
Your Turn: Complete problems 4, 8, and find the
range of 9 and 10 on pg. 160 from the Xeroxed sheets
4. 8.
9. 10.
Types of Function Behavior 3 types:
Increasing Decreasing Constant
When determining the type of behavior, we always move from left to right on the graph
Identifying Intervals of Behavior We use interval notation The interval measures x-values. The type
of behavior describes y-values.Increasing: [0, 4)
The y-values are increasing
when the x-values are between 0 inclusive and 4 exclusive
Identifying Intervals of Behavior, cont. Increasing:
Constant:
Decreasing:-1-3
y
x
Don’t get distracted by the arrows! Even though both of the arrows point “up”, the graph isn’t increasing at both ends of the graph!
Basic Types of Parent Functions1. Linear2. Absolute Value3. Greatest Integer4. Quadratic
5. Cubic6. Square Root7. Cube Root8. Reciprocal
“Baby” Functions Look and behave similarly to their parent
functions To get a “baby” functions, add, subtract,
multiply, and/or divide parent equations by (generally) constants f(x) = x2 f(x) = 5x2 – 14 f(x) = f(x) = f(x) = x3 f(x) = -2x3 + 4x2 – x + 2
x1
x24
Identifying Parent Functions From Equations:
Identify the most important operation1. Special Operation (absolute value, greatest
integer)2. Division by x3. Highest Exponent (this includes square
roots and cube roots)
Maximum (Maxima) and Minimum (Minima) PointsPeaks (or hills) are your
maximum points
Valleys are your minimum points
Identifying Minimum and Maximum Points Write the answers as
points You can have any
combination of min and max points
Minimum: Maximum:
Reminder: Find f(#) and Find f(x) = x
Find f(#) Find the value of f(x)
when x equals #. Solve for f(x) or y!
Find f(x) = # Find the value
of x when f(x) equals #.
Solve for x!
Evaluating Graphs of Functions – Find f(#)
1. Draw a (vertical) line at x = #
2. The intersection points are points where the graph = f(#)
f(1) = f(–2) =
Evaluating Graphs of Functions – Find f(x) = #
1. Draw a (horizontal) line at y = #
2. The intersection points are points where the graph is f(x) = #
f(x) = –2 f(x) = 2
Your Turn: Complete Parts A – D for problems 7 – 14
on The Key Features of Function Graphs – Part III handout.