Podcast
Questions and Answers
What defines a function?
What defines a function?
- x-values can repeat
- It has only one output for multiple inputs
- It can fail the vertical line test
- x-values do not repeat and it passes the vertical line test (correct)
What is the domain?
What is the domain?
Set of all of the possible x-values.
What is the range?
What is the range?
Set of all the possible y-values.
What is a variable?
What is a variable?
Define independent variable.
Define independent variable.
Define dependent variable.
Define dependent variable.
What are other names for 'x'?
What are other names for 'x'?
What are other names for 'y'?
What are other names for 'y'?
What is a discrete function?
What is a discrete function?
What is a continuous function?
What is a continuous function?
What does 'm' stand for in the equation y = mx + b?
What does 'm' stand for in the equation y = mx + b?
What does 'b' stand for in the equation y = mx + b?
What does 'b' stand for in the equation y = mx + b?
What is the definition of slope?
What is the definition of slope?
What slope does a horizontal line have?
What slope does a horizontal line have?
What slope does a vertical line have?
What slope does a vertical line have?
What is the x-intercept?
What is the x-intercept?
What is the y-intercept?
What is the y-intercept?
What is a linear inequality?
What is a linear inequality?
How do the slopes of parallel lines compare?
How do the slopes of parallel lines compare?
How do the slopes of perpendicular lines compare?
How do the slopes of perpendicular lines compare?
What is a line of best fit?
What is a line of best fit?
What is the solution of a system of equations?
What is the solution of a system of equations?
Where are the solutions of a quadratic function?
Where are the solutions of a quadratic function?
What are 'like terms'?
What are 'like terms'?
How do you combine like terms?
How do you combine like terms?
How do you multiply exponents of like variables?
How do you multiply exponents of like variables?
How do you divide exponents of like variables?
How do you divide exponents of like variables?
What is the rate of change on a graph?
What is the rate of change on a graph?
What is an integer?
What is an integer?
What is the Quadratic Formula?
What is the Quadratic Formula?
What is the maximum or minimum of a quadratic function?
What is the maximum or minimum of a quadratic function?
When do you flip an inequality symbol?
When do you flip an inequality symbol?
What is the Substitution Method?
What is the Substitution Method?
What is the Elimination Method?
What is the Elimination Method?
What is the solution to a system of linear inequalities?
What is the solution to a system of linear inequalities?
What is y= and f(x)=?
What is y= and f(x)=?
How do you solve when written in function notation?
How do you solve when written in function notation?
What are Geometric Sequences?
What are Geometric Sequences?
What is the Axis of Symmetry?
What is the Axis of Symmetry?
What are Linear functions?
What are Linear functions?
What are Exponential functions?
What are Exponential functions?
What is an Arithmetic Sequence?
What is an Arithmetic Sequence?
What is a positive correlation?
What is a positive correlation?
What is a negative correlation?
What is a negative correlation?
What is the Correlation Coefficient?
What is the Correlation Coefficient?
What is Causation?
What is Causation?
What is the Distributive Property?
What is the Distributive Property?
What are Perfect Squares?
What are Perfect Squares?
What is the Slope-intercept form?
What is the Slope-intercept form?
What is the Point-Slope Form?
What is the Point-Slope Form?
What is the Standard Form of a line?
What is the Standard Form of a line?
What is a Binomial?
What is a Binomial?
What is a Parabola?
What is a Parabola?
What is the Vertex of a parabola?
What is the Vertex of a parabola?
What is the maximum and minimum value in a quadratic?
What is the maximum and minimum value in a quadratic?
What is quadratic regression?
What is quadratic regression?
What is a Factor?
What is a Factor?
What does a Solid line indicate in inequalities?
What does a Solid line indicate in inequalities?
What does a Dashed line indicate in inequalities?
What does a Dashed line indicate in inequalities?
Study Notes
Functions and Variables
- A function has unique x-values that pass the vertical line test.
- Domain refers to all possible x-values of a function.
- Range includes all possible y-values.
- A variable is represented by a letter or symbol and does not equal a number.
- The independent variable is the controlled input (x-variable).
- The dependent variable is the outcome that cannot be controlled (y-variable).
Graphing and Types of Functions
- Discrete functions display data as individual points, indicating non-divisible data.
- Continuous functions show data as a smooth curve, representing divisible data.
- The graph of a linear function shows a straight line; quadratic functions form parabolic curves.
Equations and Slopes
- In the slope-intercept form (y = mx + b), (m) signifies the slope and (b) the y-intercept.
- Changing (m) alters the steepness of a line.
- Changing (b) shifts the line up or down.
- Slope is calculated as the vertical change divided by the horizontal change.
Intercepts
- The x-intercept is where a graph crosses the x-axis (coordinates ( (x, 0) )).
- The y-intercept is where it crosses the y-axis (coordinates ( (0, y) )).
Inequalities and Systems
- A linear inequality contains inequality symbols (<, >) instead of an equals sign.
- Parallel lines have equal slopes, while perpendicular lines have slopes that are opposite reciprocals.
Correlation
- Positive correlation indicates that as one variable increases, the other does as well.
- Negative correlation shows that as one variable increases, the other decreases.
- The correlation coefficient ranges from -1 to 1, reflecting the strength and direction of a relationship.
Sequences and Functions
- Geometric sequences involve multiplying or dividing by a common number.
- Arithmetic sequences involve adding a constant number each time.
- Exponential functions grow or decay at a constant factor over equal intervals.
Quadratics
- The quadratic formula is used to find solutions for quadratic equations: (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}).
- A parabola has a vertex, which indicates the maximum or minimum value.
Systems of Equations
- A system of equations contains multiple equations with the same variables.
- Solutions occur at points where the lines intersect in a system.
- Substitution and elimination methods are used to solve systems of equations.
Properties and Transformations
- The Distributive Property applies when multiplying a number across terms in parentheses.
- Transformations like vertical and horizontal translations involve shifting a graph without changing its shape.
Regression and Best Fit
- Linear regression helps find the equation of the best fit line through scatterplot data.
- Exponential regression identifies equations for exponential growth or decay.
Special Types of Lines
- A solid line indicates a solution can exist on the line (≥ or ≤).
- A dashed line indicates no solutions exist on the line (< or >).
Additional Concepts
- Positive or negative c correlations reflect a consistent relationship trend.
- An asymptote is a line that a graph approaches but never crosses.
Final Thoughts
- Understanding functions, their graphs, slopes, and intercepts is crucial in algebra.
- Knowing how to identify and manipulate equations will aid significantly in solving algebra problems.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
These flashcards provide a comprehensive review of key algebraic concepts essential for the Algebra 1 End-of-Course exam. Each card features important definitions such as function, domain, range, and variable, helping students reinforce their understanding. Perfect for quick study sessions and exam preparation.
