Algebra 2 Graphing Systems Flashcards

Study Notes

Graphing Systems of Equations

Convert equations to slope-intercept form for ease of graphing.
Graph each equation using x and y values, plotting points accurately.
The intersection of the graphs represents the solution to the system.

Systems of Equations with Simple Elimination

Cancel out either x-values or y-values to simplify the equations.
Solve for the remaining variable by isolating it on one side.
Verify the solution by substituting it back into the original equations.

Systems of Equations with Substitution

Substitute one variable into the other equation to solve.
Rearrange the equation by subtracting constants to isolate variables.
After finding the value of one variable, substitute back to solve for the other.

Systems of Equations

Utilize elimination, substitution, or graphing techniques to solve equations.
Each method provides a different approach to finding solutions effectively.

Graphing Systems with One, Zero, or Infinite Solutions

Two intersecting lines indicate a unique solution.
Parallel lines indicate no solution, as they never intersect.
Coinciding lines that overlap indicate infinite solutions.

Systems with One, Zero, or Infinite Solutions

Convert equations to slope-intercept form to analyze solutions visually.
Identify solutions based on the interaction of the lines on the graph.

Graphing Systems of Inequalities

Use dashed lines for inequalities that do not include the boundary (e.g., >).
Shade the correct area based on inequality direction: below for y greater than, above for y less than.
Solid lines indicate boundaries included in the solution (e.g., ≥).

Graphing and Solving Systems of Inequalities

Verify given points by checking if they satisfy all inequalities.
Follow graphing rules for inequalities to determine solution regions.

Systems of Nonlinear Equations

Eliminate one variable through substitution or other methods.
After substitution, graph the resulting equations (e.g., lines or parabolas).
Identify the point where the graphs intersect as the solution.

Understanding Function Notation

Interpret F(x) to determine the output y for a specific input x.
To find F(-1), locate the corresponding y-value from the graph.

Evaluating Expressions with Function Notation

Calculate the y-value for given x-values in the function.
Substitute y-values into the function to evaluate expressions.

Domain and Range from Graph

Domain refers to all possible x-values the function can take.
Range represents the lowest and highest y-values in the function's output.

Domain of a Function

Solve the inequality involving roots to find valid x-values.
Ensure denominators do not result in undefined values (like division by zero).
Roots must adhere to certain conditions depending on whether they are in the numerator or denominator.

Range of a Function

Determine the behavior of y-values based on x-value inputs.
Establish inequalities that reflect the relationships between the variables.

Evaluating Composite Functions

Substitute the output of one function as the input for another, analyzing the results.
The process involves connecting two functions in series to find overall output.

Inverses of Linear Functions

Calculate the inverse by manipulating the equation to solve for x.
Name the variables appropriately, ensuring the inverse retains correct relational properties.

Algebraically Finding Inverses

Utilize algebraic techniques to derive the inverse of a function.
Maintain focus on accurately transforming the function while understanding its graphical implications.

Description

This quiz focuses on graphing systems of equations and solving them using simple elimination methods. It provides step-by-step instructions and definitions to enhance understanding. Perfect for learners looking to master graphing and solving equations in Algebra 2.