Abeka Grade 9 Algebra 1 Quiz 40

Domain Identification for Functions

• Domain refers to the set of all possible input values (x-values) for a function.
• For the function with points (6,-3), (2,9), (-1,-3), the domain is {6, 2, -1}.
• The options for the domains of various functions:
  • For { (6,-3), (2,9), (-1,-3) }, correct domain is D: {-1,2,6}.
  • For the input-output relationship -3→7, 0↑, 9→17, correct domain is D: {-3,0,9}.
  • For f(x) = √(x+1), domain is D: {x|x≥-1}.
  • For g(x) = x + √3, the domain is all real numbers (R).
  • For h(x) = (x-1)/(x²+5x+6), domain excludes points where the denominator is zero (x≠-2, x≠-3).

Function Types and Their Parent Functions

• Identifying parent functions helps categorize different functions:
  • f(x) = 3 corresponds to a constant function (B).
  • f(x) = (1/4)x - 2 is a linear function (E).
  • f(x) = x³ + x² is categorized as a cubic function (D).
  • Various graphs represent reciprocal functions and square root functions, denoted as G and H, respectively.

Restricted Domains due to Square Roots

• Functions involving square roots have restrictions:
  • For f(x) = √(x-5)/x, x must be greater than or equal to 5 (x≥5) to keep the expression defined.
  • At the same time, x cannot equal 0 since it would create division by zero.