Abeka Grade 9 Algebra 1 Quiz 40

Identify the domain of the function { (6,-3), (2,9), (-1,-3) }. Write the letter of the correct choice in the blank.

Identify the domain of the function defined by the mappings -3→7, 0 ↑, 9→17.

Identify the domain of the function f(x) = √(x+1).

Identify the domain of the function g(x) = x + √3.

Identify the domain of the function h(x) = (x - 1) / (x² + 5x + 6).

Identify the domain of the function f(x) = (√(x-5)) / x.

Match each function with its parent function type.

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.

Test your knowledge of domain identification in functions with this Abeka grade 9 Algebra 1 quiz. Each question requires you to analyze sets of points and mathematical expressions to determine the correct domain. Show your work and choose the best answer from the provided options.