Chapter 1 8 Essential Question Essential Question What

Chapter 1 -8

Essential Question

Essential Question What is a line of symmetry?

Topic Interpreting graphs of function including intercepts, positive, negative, increasing, decreasing, extrema, and end behavior

Definitions Intercepts – where the graph crosses the x and y axis

Definitions Intercepts – where the graph crosses the x and y axis Line of symmetry – if each half of the graph matches the other half when folded on a line

Definitions Intercepts – where the graph crosses the x and y axis Line of symmetry – if each half of the graph matches the other half when folded on a line Positive – graph above the x-axis

Definitions Intercepts – where the graph crosses the x and y axis Line of symmetry – if each half of the graph matches the other half when folded on a line Positive – graph above the x-axis Negative – graph below the y-axis

Definitions Intercepts – where the graph crosses the x and y axis Line of symmetry – if each half of the graph matches the other half when folded on a line Positive – graph above the x-axis Negative – graph below the y-axis Increasing – from left to right the graph is going up

Definitions Intercepts – where the graph crosses the x and y axis Line of symmetry – if each half of the graph matches the other half when folded on a line Positive – graph above the x-axis Negative – graph below the y-axis Increasing – from left to right the graph is going up Decreasing – from left to right the graph is going down

Cont. Extrema Relative minimum – the lowest point on the graph

Cont. Extrema Relative minimum – the lowest point on the graph Relative maximum – the highest point on the graph

Cont. Extrema Relative minimum – the lowest point on the graph Relative maximum – the highest point on the graph End Behavior Sketch negative odd function – as x increases, y decreases and as x decreases, y increases

Cont. Extrema Relative minimum – the lowest point on the graph Relative maximum – the highest point on the graph End Behavior Sketch negative odd function – as x increases, y decreases and as x decreases, y increases Sketch negative even function – as x increases, y decreases and as x decreases, y decreases

Ex. 1 The graph shows the cost at a community college y as a function of the number of credit hours taken, x. Identify the functions as linear or nonlinear. Then estimate and interpret the intercepts of the graph.

Ex. 1 The graph shows the cost at a community college y as a function of the number of credit hours taken, x. Identify the functions as linear or nonlinear. Then estimate and interpret the intercepts of the graph. No x intercept; y intercept is at 50

Ex. 2 The graph shows the outbreak of the H 1 N 1 virus. Estimate and interpret where the function is positive, negative, increasing, decreasing, the x coordinate of any relative extrema and end behavior.

Ex. 2 cont. Positive – for x between 0 and 42

Ex. 2 cont. Positive – for x between 0 and 42 Negative – none

Ex. 2 cont. Positive – for x between 0 and 42 Negative – none Increasing – for x between 0 and 42

Ex. 2 cont. Positive – for x between 0 and 42 Negative – none Increasing – for x between 0 and 42 Decreasing – none

Ex. 2 cont. Positive – for x between 0 and 42 Negative – none Increasing – for x between 0 and 42 Decreasing – none Relative maximum – x = 42

Ex. 2 cont. Positive – for x between 0 and 42 Negative – none Increasing – for x between 0 and 42 Decreasing – none Relative maximum – x = 42 Relative minimum – x = 0

Ex. 2 cont. Positive – for x between 0 and 42 Negative – none Increasing – for x between 0 and 42 Decreasing – none Relative maximum – x = 42 Relative minimum – x = 0 End behavior – as x increases, y approaches 12000

Ex. 3 This graph shows price variations on stock prices. Determine where the graph is positive, negative, increasing, decreasing, extrema, and end behavior.

Ex. 3 cont. Positive – x value 5 and greater

Ex. 3 cont. Positive – x value 5 and greater Negative – x value between 0 and 5

Ex. 3 cont. Positive – x value 5 and greater Negative – x value between 0 and 5 Increasing – x greater than 3

Ex. 3 cont. Positive – x value 5 and greater Negative – x value between 0 and 5 Increasing – x greater than 3 Decreasing – x between 0 and 3

Ex. 3 cont. Positive – x value 5 and greater Negative – x value between 0 and 5 Increasing – x greater than 3 Decreasing – x between 0 and 3 Relative maximum – x = 6

Ex. 3 cont. Positive – x value 5 and greater Negative – x value between 0 and 5 Increasing – x greater than 3 Decreasing – x between 0 and 3 Relative maximum – x = 6 Relative minimum – x = 3

Ex. 4 The graph shows the area y in square centimeters of a rectangle with perimeter 20 centimeters and width x centimeters. Describe and interpret any symmetry in the graph.

Ex. 4 cont. Relative maximum – x = 5

Ex. 4 cont. Relative maximum – x = 5 Symmetric with left half mirror image of the right half

Ex. 4 cont. Relative maximum – x = 5 Symmetric with left half mirror image of the right half Symmetry tells you that as x increases to the maximum or decreases from the maximum, area will be the same

Ex. 5 The graph is the deer population introduced on an island. Interpret the graph.

Ex. 5 cont. y intercept – 75 (initial population)

Ex. 5 cont. y intercept – 75 (initial population) Positive between 0 and 5. 5 (deer died out before the end of year 6)

Ex. 5 cont. y intercept – 75 (initial population) Positive between 0 and 5. 5 (deer died out before the end of year 6) Decreased year 1

Ex. 5 cont. y intercept – 75 (initial population) Positive between 0 and 5. 5 (deer died out before the end of year 6) Decreased year 1 Relative maximum – x = 4

Ex. 5 cont. y intercept – 75 (initial population) Positive between 0 and 5. 5 (deer died out before the end of year 6) Decreased year 1 Relative maximum – x = 4 Relative minimum – x = 5. 5

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