Unit 1 Day 1 Key Features of Graphs F-IF.4: Interpret key features of graphs, tables, and verbal descriptions in context to describe functions that arise in applications relating two quantities to include periodicity and discontinuities.

Domain and Range of Graphs When identifying domain and range from a graph, you will write your answer as an _____________ Domain (from ________ to _________) Smallest x-value to largest x-value Range (from ________ to _________) Smallest y-value to largest y-value Use a ____________________( or ) for an open dot Use a ____________________[ or ] for a closed dot If this graph continues forever in any direction, use ∞ (______________) in place of a number interval left right bottom top Soft bracket Hard bracket infinity

Identify the domain and range of the graph below: [ −4, 6 ] [ −4, 3 ]

Intervals of Increase/Decrease To determine whether a graph is increasing or decreasing look ____________ (like you’re reading) When the graph goes up (left to right) this graph is __________ When the graph goes down (left to right) the graph is ______________ When writing intervals of increase/decrease only look at the _________ and only use ____________ () left to right increasing decreasing x-values soft brackets

Identify the intervals of increase/decrease for the graph: Increasing: Decreasing: ( −1, 3 ) ( −4, −1 ) U( 3, 6 )

Intervals where Functions is Positive/Negative The positive regions of a function are those intervals where the function is _____________ the __________.  It is where the y-values are ____________. The negative regions of a function are those intervals where the function is ________ the _______.  It is where the y-values are__________. above x-axis positive below x-axis negative

Identify the intervals where the function is positive and the intervals where it is negative ( −4, −3 ) U( 1, 5 ) ( −3, 1 ) U( 5, 6 )

Maximum/Minimum Absolute max/min: the highest (_______) or lowest (_______) y-value on a graph Relative max/min: the highest (_____________) or lowest (_______________) y-value on the graph compared to the surrounding points max min relative max relative min

Identify the max/min of the graph below Identify the max/min of the graph below. Determine if these points are absolute or relative: Maximum: ______ Absolute or Relative Minimum: _______ 3 −4

X-Intercepts Where the graph crosses the __________ (horizontal axis) X-intercepts are also called the ______________ or zeros of the function x-axis solutions What are the x-intercepts or solutions of the function graphed to the right? (−3, 0) (1, 0) (5, 0)

Identify the Key Features of the Graph Below Example #1 Identify the Key Features of the Graph Below Domain: Range: Increasing: Decreasing: Maximum: Absolute or Relative Minimum: Absolute or Relative X-intercept(s): Is the graph a function? ( −4, ∞ ) ( −∞, 4 ] (−2, 2) (−4, −2) U(2, ∞) 4 −4 0, 3 Yes

Identify the Key Features of the Graph Below Example #2 Identify the Key Features of the Graph Below Domain: Range: Increasing: Decreasing: Maximum: Absolute or Relative Minimum: Absolute or Relative X-intercept(s): Is the graph a function? [ 0, 10 ] [ 0, 7 ] (0, 3) (7, 10) 7 0, 10 yes

Identify the Key Features of the Graph Below Example #3 Identify the Key Features of the Graph Below Domain: Range: Increasing: Decreasing: Maximum: Absolute or Relative Minimum: Absolute or Relative X-intercept(s): Is the graph a function? ( −∞, ∞ ) ( −∞, ∞ ) (−∞, ∞) Never None None yes

Identify the Key Features of the Graph Below Example #4 Identify the Key Features of the Graph Below Domain: Range: Increasing: Decreasing: Maximum: Absolute or Relative Minimum: Absolute or Relative X-intercept(s): Is the graph a function? ( −∞, ∞ ) ( 0, ∞ ) (−∞, ∞) Never None None None yes

Identify the Key Features of the Graph Below Example #5 Identify the Key Features of the Graph Below Domain: Range: Increasing: Decreasing: Maximum: Absolute or Relative Minimum: Absolute or Relative [ −5, 1 ] U ( 2, 5 ] [ −2, 4 ] (−2, 0) (0, 1) U(2, 5) 4 −2