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...
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.
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller jesussanchez9306. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $20.49. You're not tied to anything after your purchase.
