Interpreting Graphs of Functions: Key Concepts and Techniques

The video tutorial covers interpreting graphs of functions, focusing on key concepts such as x-intercepts, y-intercepts, line symmetry, positive and negative functions, increasing and decreasing functions, relative maximums and minimums, and end behavior. The instructor provides definitions and visual examples to illustrate these concepts, emphasizing the importance of reading graphs from left to right. The tutorial concludes with a detailed example, analyzing a graph's intercepts, extrema, and behavior as it approaches infinity.

What is an x-intercept?

• A point where the graph crosses the y-axis

• A point where the graph reaches its minimum

• A point where the graph reaches its maximum

• A point where the graph crosses the x-axis

What does line symmetry in a graph mean?

• The graph has no symmetry

• The left and right halves of the graph are mirror images

• The graph is symmetrical around the x-axis

• The graph is symmetrical around the y-axis

Where is a positive function located on a graph?

• Above the y-axis

• Below the x-axis

• Below the y-axis

• Above the x-axis

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5

How do you identify a negative function on a graph?

• It is above the y-axis

• It is above the x-axis

• It is below the x-axis

• It is below the y-axis

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CCSS.HSF.IF.A.3

How do you read an increasing function on a graph?

• From right to left

• From top to bottom

• From bottom to top

• From left to right

What does a decreasing function look like on a graph?

• The graph goes up and to the left

• The graph goes down and to the right

• The graph goes down and to the left

• The graph goes up and to the right

What is a relative maximum?

• A point where the graph reaches a low value

• A point where the graph reaches a high value

• A point where the graph crosses the x-axis

• A point where the graph crosses the y-axis

What is a relative minimum?

• A point where the graph reaches a low value

• A point where the graph reaches a high value

• A point where the graph crosses the y-axis

• A point where the graph crosses the x-axis

What does end behavior describe?

• The behavior of the graph at its intercepts

• The behavior of the graph at its maximum points

• The behavior of the graph at its minimum points

• The behavior of the graph as it approaches infinity

What happens to the graph as x approaches positive infinity in the final example?

• y approaches negative infinity

• y approaches positive infinity

• y remains constant

• y oscillates