Abeka Grade 9 Algebra 1 Test 10 Flashcards

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Questions and Answers

A relation is a collection of _____

set

The range is the set of the _____ of a relation.

inputs

A function is a relation in which every allowable input has exactly one output.

True

The equation $x²=y+8$ expressed as a function would be $f(x)=x²-8$.

True Signup and view all the answers

Write the equation of the function graphed below in function notation.

f(x) = ³√x + 2 - 1√√ Signup and view all the answers

Write the domain and range of the function graphed below.

(a) D: R; (b) R: {f(x) | f(x) ≥ -4} Signup and view all the answers

What is the domain of { (3,-3), (-5,-3), (3,0) }?

D: {-5,3} Signup and view all the answers

What is the range of the mapping diagram on the right?

R: {0,1,2,3,4} Signup and view all the answers

Which of these sets of ordered pairs is a function?

{(2,3), (0,3), (9,-2)} Signup and view all the answers

Which of these graphs is a function?

a Signup and view all the answers

Determine how much the function $g(x) = 1/x +4$ has been translated from its parent function.

up 4 Signup and view all the answers

Match each function with its parent function type.

f(x) = (x-1)³ = cubic f(x) = 2x²+5 = quadratic graph = absolute value Signup and view all the answers

For the function $f(x) = x³-4x$, find $f(4)$.

$f(4) = 48$ Signup and view all the answers

What is the domain of $f(x) = 5 / (x-5)$?

D: {x|x≠5} Signup and view all the answers

What is the domain of $g(x) = x²+x$?

D: R Signup and view all the answers

What is the domain of $h(x) = √(x+6) / x$?

D: {x|x≥-6, x≠0} Signup and view all the answers

What is the domain of $f(x) = x / (x²-3x+2)$?

D: {x|x≠0,1,2} Signup and view all the answers

Find the missing side in the triangle using the appropriate trigonometric function.

2.05 Signup and view all the answers

Match each trigonometric function with its value based on the given triangle.

sin(A) = 3/5 cos(A) = 4/5 tan(A) = 3/4 sin(B) = 4/5 cos(B) = 3/5 tan(B) = 4/3 Signup and view all the answers

Sketch the graph of the function using your knowledge of parent functions: $f(x) = √(x+4) + 3$.

Sketch of transformed square root function. Signup and view all the answers

Study Notes

Relations and Functions

A relation is defined as a collection of ordered pairs, specifically a set, not just objects.
The range consists of outputs while the domain is the set of inputs in a relation.
A function is a special type of relation where each input corresponds to exactly one output.

Function Equations

The function f(x)=x²-8 can be derived from the equation x²=y+8, confirming its correct expression as a function.
Function notation can be verified through graphing, which requires expressing equations accurately.

Domain and Range

The domain (D) and range (R) must be identified for functions based on their graphs.
For a specified function, the domain might be D: R (all real numbers), while the range could include numbers greater than or equal to a specific value (e.g., -4).

Multiple Choice for Domains and Ranges

When presented with sets of ordered pairs, the domain is found by identifying unique x-values.
The range is determined by finding unique y-values in a mapping diagram.

Functions and Their Properties

Sets of ordered pairs must be evaluated to determine if they represent a function; a function requires unique x-values.
Specific graphs can be classified as functions based on the vertical line test.

Translations of Functions

The transformation of functions can be analyzed through changes in their equations, such as vertical shifts indicated by constants added or subtracted.

Parent Function Matching

Functions can be categorized according to their parent types, such as linear, quadratic, cubic, absolute value, and cube root functions.

Evaluating Functions

To evaluate functions such as f(x) = x³ - 4x at specific points (e.g., f(4)), perform the necessary calculations to find the resultant value.

Domain Restrictions

Determining the domain often requires excluding certain values, such as values that make the denominator zero or are not allowed under square root operations.
Example: For f(x) = 5/(x-5), the domain excludes x-values that make the denominator zero.

Trigonometric Functions

To find missing sides in right triangles, apply appropriate trigonometric functions (sine, cosine, tangent).
The sine, cosine, and tangent values of angles can be matched to their respective ratios based on triangle dimensions.

Graph Sketching

When graphing functions, utilize knowledge of parent functions to sketch the graph accurately, adjusting for any transformations applied to the original function.

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Description

Test your knowledge with Abeka's Grade 9 Algebra 1 Test 10 flashcards. This quiz covers key concepts such as relations, functions, and their definitions, ensuring you grasp the fundamentals essential for your Algebra studies. Ideal for review and preparation for upcoming assessments.