Determining the Key Features of Function Graphs
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 To find the domain of the graph _____________________ of the graph
Determining Domain - Symbols → →
Determining Domain 1. Start at the origin Return to the origin 4.
Examples Domain:
Example Domain:
Determining Domain - Infinity Domain:
Examples Domain:
Your Turn: In the purple Precalculus textbooks, complete problems 3, 7, and find the domain of 9 and 10 on pg
Range To find the range of the graph _____ _________________of the graph We also use open and closed circles for the range
Determining Range 1. Start at the origin Return to the origin 4.
Examples Range:
Examples Range:
Your Turn: In the purple Precalculus textbooks, complete problems 4, 8, and find the range of 9 and 10 on pg
X-Intercepts Has many names: x-intercept Roots Zeros
Examples x-intercepts:
Y-Intercepts y-intercepts:
Seek and Solve!!!
Types of Function Behavior 3 types: Increasing Decreasing Constant When determining the type of behavior, __________________________________ __________________________________
Roller Coasters!!! Fujiyama in Japan
Types of Behavior – Increasing Direct Relationship
Types of Behavior – Constant
Types of Behavior – Decreasing Inverse Relationship
Identifying Intervals of Behavior Increasing: [0, 4) The y-values are increasing when the x-values are between 0 inclusive and 4 exclusive
Identifying Intervals of Behavior Increasing: Constant: Decreasing: x 1 1 y
Identifying Intervals of Behavior, cont. Increasing: Constant: Decreasing: -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!
Your Turn: Complete problems 1 – 4 on The Key Features of Function Graphs – Part II handout.
What do you think of when you hear the word parent?
Parent Function Flipbook
Parent Function The most basic form of a type of function Determines the general shape of the graph
Basic Types of Parent Functions 1. Linear 2. Absolute Value 3. Greatest Integer 4. Quadratic 5. Cubic 6. Square Root 7. Cube Root 8. Reciprocal
Function Name: Linear Parent Function: f(x) = x “Baby” Functions: f(x) = 3x f(x) = x + 6 f(x) = –4x – 2 y x2 2
Greatest Integer Function f(x) = [[x]] f(x) = int(x) Rounding function Always round down
“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) = x 2 f(x) = 5x 2 – 14 f(x) = f(x) = f(x) = x 3 f(x) = -2x 3 + 4x 2 – x + 2
“Baby” Functions, cont. f(x) = |x|
Your Turn: Create your own “baby” functions in your parent functions book.
Identifying Parent Functions From Equations: Identify the most important operation 1. Special Operation (absolute value, greatest integer) 2. Division by x 3. Highest Exponent (this includes square roots and cube roots)
Examples 1. f(x) = x 3 + 4x – 3 2. f(x) = -2| x |
Identifying Parent Equations From Graphs:
Examples
Your Turn: Complete problems 5 – 12 on The Key Features of Function Graphs handout
Maximum (Maxima) and Minimum (Minima) Points
Identifying Minimum and Maximum Points You can have any combination of min and max points Minimum: Maximum:
Examples
Your Turn: Complete problems 1 – 6 on The Key Features of Function Graphs – Part III handout.
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(#) f(1) = f(–2) =
Evaluating Graphs of Functions – Find f(x) = # f(x) = –2 f(x) = 2
Example 1. Find f(1) 2. Find f(–0.5) 3. Find f(x) = 0 4. Find f(x) = –5
Your Turn: Complete Parts A – D for problems 7 – 14 on The Key Features of Function Graphs – Part III handout.