Algebra 1 Flashcards

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Questions and Answers

What is a relation?

A relation pairs inputs with outputs. When a relation is given as ordered pairs, the x-coordinate is the input and y-coordinate is the output.

What is a function?

A relation that pairs each input with exactly one output.

What is the vertical line test?

A graph represents a function when no vertical line passes through more than one point on the graph.

What is the domain of a function?

A set of all possible input values. Signup and view all the answers

What is the range of a function or relation?

A set of all possible output values. Signup and view all the answers

How can a linear equation in two variables be expressed?

In the form y = mx + b. Signup and view all the answers

Is y = 6 a linear function?

True Signup and view all the answers

Is y = x^2 + 6 a linear function?

False Signup and view all the answers

All linear functions are linear equations.

True Signup and view all the answers

What are the characteristics of a linear function?

<ol> <li>Has a single output for a given input. 2. The same input cannot produce a different output on different occasions. 3. The graph is a line. 4. A straight line through the graph may not intersect in more than one point. 5. Represents a constant rate of change. 6. Can be expressed in the form y = mx + b.</li> </ol> Signup and view all the answers

What is the difference between discrete and continuous domain?

Discrete domain consists of certain numbers in an interval, while continuous domain consists of all numbers in an interval. Signup and view all the answers

What is the x-intercept?

The x-coordinate of a point where a graph crosses the x-axis. Signup and view all the answers

How many points are needed on a linear equation graph to determine the solution set?

Two. Signup and view all the answers

What is the slope of a non-vertical line?

Rise over run. Signup and view all the answers

What is a constant function?

A function whose graph is a horizontal line, expressed as y = b. Signup and view all the answers

What is the slope-intercept form of a line?

y = mx + b. Signup and view all the answers

What is the y-intercept?

The value of y when x = 0. Signup and view all the answers

When are two non-vertical lines parallel?

When they have the same slope. Signup and view all the answers

When are two non-vertical lines perpendicular?

If their slopes are negative reciprocals. Signup and view all the answers

What is a quadratic function?

A nonlinear function that can be written in the standard form y = ax^2 + bx + c, where a ≠ 0. Signup and view all the answers

Study Notes

Relations and Functions

A relation pairs inputs with outputs; represented as ordered pairs (x, y).
A function is a specific type of relation where each input corresponds to exactly one output.
Different inputs may have the same output in a function, but any input must always map to one output.

Graphing Functions

The vertical line test determines if a graph represents a function. If any vertical line intersects the graph at more than one point, it is not a function.
The domain of a function includes all possible input values.
The range of a function includes all possible output values.

Linear Functions and Equations

A linear equation can be expressed as y = mx + b, where m (slope) and b (y-intercept) are constants. Its graph is a straight line.
A linear function is an equation in two variables that graphs to a non-vertical line and maintains a constant rate of change.
The equation y = 6 is a linear function because it can be rewritten as y = 0x + 6. Conversely, y = x^2 + 6 is not linear as it cannot be expressed in linear form.

Characteristics and Types of Functions

True/False: All linear functions are linear equations—True; not all linear equations are functions, particularly those graphing vertical lines.
Characteristics of a linear function include:
- A single output for each input.
- Consistency: the same input gives the same output.
- A line graph that does not intersect itself at more than one point.
- Representing a constant rate of change.

Domain Types

Discrete domain consists of specific input values, while a continuous domain includes all numbers within an interval.
Understanding whether a domain is discrete or continuous often requires context beyond the equation.

Intercepts and Slope

The x-intercept is where the graph crosses the x-axis, identified by its x-coordinate.
To identify a linear equation's solution set, two points are required due to the constant rate of change.
The slope of a non-vertical line is calculated as "rise over run."

Function Forms

A constant function is visually a horizontal line and can be represented as y = b.
Slope-intercept form, y = mx + b, specifies m as the slope and b as the y-intercept, which represents the output when x = 0.
Point-slope form is written as y2 - y1 = m(x2 - x1).

Line Relationships

Non-vertical lines are parallel if they have the same slope. Vertical lines are inherently parallel with a slope of 0.
Lines are perpendicular if the slopes are negative reciprocals; horizontal and vertical lines are always perpendicular.

Quadratic Functions

A quadratic function is nonlinear, represented in standard form as y = ax² + bx + c, with a non-zero value of a.

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Description

Test your knowledge of key concepts in Algebra 1 with these flashcards. Each card provides a definition for essential terms such as relations and functions. Perfect for quick review and self-assessment.