Characteristics of Functions

Slides:

Advertisements

Similar presentations

Find the solutions. Find the Vertex and Max (-1, 0) (5, 0) (2, 10)

Advertisements

Analysis of Linear Functions. Trick Question? #6 x = ? This is a VERTICAL line. Slope (m) – UNDEFINED Steepness – MORE or NO Solution Y intercept (b)

MATH 140 January 18, The Graph of a Function When a function is defined by an equation in x and y, the graph of a function is the set of all points.

EXAMPLE 3 Write an equation of a line given two points

17, 13, 9, 5, … 1.Write the rule for the above sequence. 2.What is the 12 th term? is what term in the sequence?

Identifying Features of Linear and Exponential Functions S tandard: A.F.IF.4 Essential Question: How do I identify key features from a graph of a linear.

Parent Functions 4.4 Transformations 4.5 Inverse Functions 4.6 Average Rate of Change Secondary Math 2 4.1/4.2 Functions

X-intercept(s): y-intercept: Domain: Axis of Symmetry: Zero(s): Range: What are the Characteristics of Quadratic Functions?? MM2A3c. Investigate and explain.

Essential Skills & Linear Functions Complex Numbers Solving Quadratic Equations Quadratic Functions Polynomials.

Slope (Finding it from a graph.). Key Idea : Slope of a line is a ratio of change in y (the rise) to the change in x (the run) between any two points.

EXAMPLE 5 Find the zeros of quadratic functions. Find the zeros of the function by rewriting the function in intercept form. a. y = x 2 – x – 12 b. y =

Functions. Objectives: Find x and y intercepts Identify increasing, decreasing, constant intervals Determine end behaviors.

Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? That’s your domain! Range- Look vertically: What y-values.

Characteristics of Quadratic functions f(x)= ax 2 + bx + c f(x) = a (x – h) 2 + k.

Pay attention in class.

What is the terminology we use to analyze a quadratic function?

Slope Slope is the steepness of a straight line..

Family Functions: Increasing and Decreasing End Behavior

Attributes of functions in their graph

6.2 Using Intercepts.

Estimate and classify the extrema for f (x)

Properties of Functions

Standard MM2A3. Students will analyze quadratic functions in the forms f(x) = ax2 + bx + c and f(x) = a(x – h)2 + k. c. Investigate and explain characteristics.

Chapter 1: Lesson 1.5 Analyzing Graphs of Functions

Characteristics of Functions

Warm up 1.a. Write the explicit formula for the following sequence

Warm Up Find the equation of a line with slope of 4 passing through the point (-1, 6). James is driving at an average speed of 60 miles per hour. He wanted.

Characteristics of Quadratic functions

Graphing Linear Equations by the intercept method

5-Minute Check Lesson 1-3A

Parallel Lines: SLOPES ARE THE SAME!!

AP Calculus November 9-10, 2016 Mrs. Agnew

3.1: Increasing and Decreasing Functions

Characteristics of Linear Graphs

8.6.4 Comparing Linear and Nonlinear Functions

3.5 Write and Graph Equations of Lines

What can you tell me about this graph?

Characteristics OF EXPONENTIAL FUNCTIONS!!!!!.

Functions AII.7 cdf 2009.

Warm-up Name the domain and range for the following:

Characteristics of Quadratic functions

Characteristics of Functions

Characteristics of Functions

Warm-up Name the following functions. Quadratic Cubic Absolute Value.

Section 2.3 – Analyzing Graphs of Functions

Section 4.4 – Analyzing Graphs of Functions

Skill Check after HW Check

Pre-Calculus Go over homework Notes: Increasing and Decreasing

Characteristics of Quadratic functions

Domain and Range Domain- x-values - input Range- y-values - output D comes before R like x comes before y.

Analyzing Graphs of Functions

Pre-Calculus Go over homework End behavior of a graph

55. Graphing Exponential Functions

Characteristics.

Silent Do Now (5 minutes) *Before you begin, take out your homework!

5 Minute Check 1-4 Graph the equation : 2x + y – 4 = 0

Characteristics of Functions

Characteristics.

Warm up Write the equation in vertex form of the quadratic equation that has been: 1. shifted right 7 and down reflected across the x-axis and shifted.

Average Rate of Change.

Characteristics of Quadratic functions

5.3 Polynomial Functions.

Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

y = -.5x + 4 for X > -2 y = 2x + 1 for X ≤ -2 Warm Up

Characteristics of Quadratic functions

Presentation transcript:

Characteristics of Functions

Intercepts (aka “zeros”) x-intercept – the point at which the line intersects the x-axis at (x, 0) y-intercept – the point at which the line intersects the y-axis at (0, y)

Example 1: Finding the Zeros

Example 2: Find the y-intercept

Increasing/Decreasing Behavior Move left to right If your finger is moving UP then the function is increasing If your finger is moving DOWN then the function is decreasing If your finder isn’t moving up or down, than your function is CONSTANT

Example 1: Are the functions increasing, decreasing or neither?

Rate of Change Rate of Change is the average amount of change in her y-values. Rate of Change is essentially the SLOPE.

Example: Rate of Change with Points Find the rate of change, given the following points: (2,3) and (1,4)

Example: Rate of Change with functions Find the average rate of change for f(x) = ½x + 4 from [0,3]

Guided Practice