Algebra 1 EOC Review (2022) Flashcards

Questions and Answers

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?

Set of all of the possible x-values.

What is the range?

Set of all the possible y-values.

What is a variable?

Not a number, a letter or symbol that stands for a number. Signup and view all the answers

Define independent variable.

The input or cause in a situation or problem. Signup and view all the answers

Define dependent variable.

The output or result in a situation or problem. Signup and view all the answers

What are other names for 'x'?

Input Signup and view all the answers

What are other names for 'y'?

Output Signup and view all the answers

What is a discrete function?

Data appears as individual points on a graph. Signup and view all the answers

What is a continuous function?

Data appears as a smooth curve on a graph. Signup and view all the answers

What does 'm' stand for in the equation y = mx + b?

Slope Signup and view all the answers

What does 'b' stand for in the equation y = mx + b?

The y-intercept Signup and view all the answers

What is the definition of slope?

The steepness of a line. Signup and view all the answers

What slope does a horizontal line have?

Slope = 0 Signup and view all the answers

What slope does a vertical line have?

Undefined slope Signup and view all the answers

What is the x-intercept?

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

What is the y-intercept?

The point where the graph crosses the y-axis. Signup and view all the answers

What is a linear inequality?

An equation with a < or =, > or = in place of the = Signup and view all the answers

How do the slopes of parallel lines compare?

They are the same. Signup and view all the answers

How do the slopes of perpendicular lines compare?

They are opposite reciprocals. Signup and view all the answers

What is a line of best fit?

A line drawn through the points on a scatterplot. Signup and view all the answers

What is the solution of a system of equations?

Where the lines touch or cross. Signup and view all the answers

Where are the solutions of a quadratic function?

At the x-intercepts. Signup and view all the answers

What are 'like terms'?

Mathematical terms that have the same variables raised to the same exponents. Signup and view all the answers

How do you combine like terms?

Add their coefficients. Signup and view all the answers

How do you multiply exponents of like variables?

Add them. Signup and view all the answers

How do you divide exponents of like variables?

Subtract them. Signup and view all the answers

What is the rate of change on a graph?

Slope Signup and view all the answers

What is an integer?

A whole number, both positive and negative numbers. Signup and view all the answers

What is the Quadratic Formula?

x = -b ± √(b² - 4ac)/2a Signup and view all the answers

What is the maximum or minimum of a quadratic function?

The highest or lowest point of a parabola. Signup and view all the answers

When do you flip an inequality symbol?

Anytime you multiply or divide by a negative number. Signup and view all the answers

What is the Substitution Method?

Solving one equation for one variable and plugging it into another. Signup and view all the answers

What is the Elimination Method?

Manipulation is needed in order for x-values or y-values to cancel each other out. Signup and view all the answers

What is the solution to a system of linear inequalities?

The intersection of the two half-planes. Signup and view all the answers

What is y= and f(x)=?

These are the same. Signup and view all the answers

How do you solve when written in function notation?

Replace x with (-2) and solve. Signup and view all the answers

What are Geometric Sequences?

A pattern in which you multiply or divide by a common number. Signup and view all the answers

What is the Axis of Symmetry?

The equation x=0 is the axis of symmetry for a parabola in standard form. Signup and view all the answers

What are Linear functions?

A function that has only one answer for y for every x. Signup and view all the answers

What are Exponential functions?

Functions where the variable is the exponent. Signup and view all the answers

What is an Arithmetic Sequence?

A pattern in which you add a number each time. Signup and view all the answers

What is a positive correlation?

A relationship where one variable increases as the other also increases. Signup and view all the answers

What is a negative correlation?

A relationship where one variable increases and the other decreases. Signup and view all the answers

What is the Correlation Coefficient?

A number between -1 and 1 that indicates strength and direction of correlation. Signup and view all the answers

What is Causation?

The reason something occurs. Signup and view all the answers

What is the Distributive Property?

Multiply a number or variable to everyone inside parentheses. Signup and view all the answers

What are Perfect Squares?

1, 4, 9, 16, 25, etc. Signup and view all the answers

What is the Slope-intercept form?

y = mx + b Signup and view all the answers

What is the Point-Slope Form?

(y - y*) = m (x - x*) Signup and view all the answers

What is the Standard Form of a line?

Ax + By = C Signup and view all the answers

What is a Binomial?

A polynomial with two terms. Signup and view all the answers

What is a Parabola?

The shape of the graph of a quadratic function. Signup and view all the answers

What is the Vertex of a parabola?

The lowest or highest point on a parabola. Signup and view all the answers

What is the maximum and minimum value in a quadratic?

The highest or lowest output of a quadratic function. Signup and view all the answers

What is quadratic regression?

y1 ~ ax1^2 + bx1 + c Signup and view all the answers

What is a Factor?

A binomial that is multiplied by another binomial to find a product. Signup and view all the answers

What does a Solid line indicate in inequalities?

≤ or ≥, can be a solution if on the line. Signup and view all the answers

What does a Dashed line indicate in inequalities?

< or >, can't be a solution if on the line. Signup and view all the answers

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.

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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.