Class notes

Class notes Math - Precalculus Algebra

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Course
Math - Precalculus Algebra

Institution
Wake Technical Community College

This comprehensive document is designed to help learners master the interpretation of various types of mathematical graphs, with a focus on analyzing and understanding the key features of functions. The material covers essential skills such as determining the domain and range of a function and util...

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Uploaded on October 5, 2024
Number of pages 6
Written in 2024/2025
Type Class notes
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mat171 interpreting graphs 1

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1

MAT171 Interpreting Graphs 1
Learning Objectives: The learner will be able to:
• From the graph of a function determine its domain and range and analyze the graph for intervals of
increase/decrease, and continuity and state each using interval notation
• Determine maximum/minimum values (local and absolute); output given input, input given output, and
intervals where a graph is greater than/less than/equal to zero or another value
• From the graph of a relation use the vertical line test to determine if it is a function, and if it is a function use
the horizontal line test to determine if it is a one-to-one function
• Use typical naming conventions ie linear, quadratic, polynomial, exponential, logarithmic, rational, radical,
piecewise, and absolute value to associate the graph of a function with its name and symbolic form as well
as describe the basic properties of these functions.

Definitions

The _________________ of a function is the set of all _____________ for the function.

The _________________ of a function is the set of all ______________ associated with the inputs in
the domain.

Example: Determine the domain and range of the functions. Write your answer in inequality
notation and in interval notation.

Inequality Notation:

Domain:________________________

Range: _________________________

Interval Notation:

Domain:________________________

Range: _________________________

Determine domain and range in interval
notation:

Domain:________________________

Range: _________________________

, 2
Definitions

A __________________ f is a relation between two sets. A function is a rule that assigns to each
element in the first set _____________ one element in the second set. The first set is called the
______________ of the function. The second set is called the _________________ of the function.

The _______________________ variable is the variable associated with the domain; the
_____________________ variable belongs to the range.

Example: Determine whether the relation represents y as a function of x.

The Vertical Line Test
A graph represents a function if and only if every _______________ line intersects the graph at most
________. A graph that fails this test does ________ represent a function.

Example: Use the Vertical Line test to decide whether each of the following graphs represents y as a
function of x.

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