ALGRZ.MATH.3.A

Compare and contrast the key attributes, including domain, range, maxima, minima, and intercepts, of a set of functions such as a set comprised of a linear, a quadratic, and an exponential function or a set comprised of an absolute value, a quadratic, and a square root function tabularly, graphically, and symbolically.

Algebraic Reasoning · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

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Vocabulary
key attributesdomainrangemaximaminimainterceptsfunctionslinear functionquadratic functionexponential functionabsolute value functionsquare root functionrepresentationtablegraphsymbol
Skills
  • compare (key attributes of functions tabularly, graphically, and symbolically) #dok2
  • contrast (key attributes of functions tabularly, graphically, and symbolically) #dok2
  • identify (domains, ranges, maxima, minima, and intercepts of functions in multiple representations) #dok1
  • analyze (differences in function attributes among various function types) #dok3
  • interpret (tables, graphs, and symbolic representations of functions) #dok2
Learning Targets
  • I can identify the domain, range, maxima, minima, and intercepts of a function from a table, graph, or equation. #dok1
  • I can list the key attributes of linear, quadratic, and exponential functions in different representations. #dok1
  • I can compare the domain and range of two different types of functions using tables, graphs, and equations. #dok2
  • I can contrast the intercepts, maxima, and minima of different functions across representations. #dok2
  • I can interpret tables, graphs, and equations to determine how key attributes differ between functions. #dok2
  • I can analyze multiple representations to draw conclusions about the similarities and differences among linear, quadratic, exponential, absolute value, and square root functions. #dok3
  • I can justify how key attributes can be observed or explained through tables, graphs, or equations. #dok3
Big Ideas
  • The key attributes of functions—such as domain, range, maxima, minima, and intercepts—help us understand and compare different types of functions.
  • Representing functions in various ways (tables, graphs, symbols) reveals similarities and differences in their key attributes.
Essential Questions
  • How do the key attributes (domain, range, maxima, minima, intercepts) of different types of functions compare and contrast?
  • In what ways do table, graph, and equation representations each reveal information about a function’s characteristics?
  • How can you determine if two different functions have similar or different ranges or intercepts from their representations?
  • Why might certain attributes (like maxima or minima) be easier to find in one representation versus another?
  • What can the similarities or differences in key attributes tell us about the relationship between different types of functions?