Algebra 1: Variables and Equations Flashcards
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Questions and Answers

What is the term for a variable that relies on nothing?

Independent Variable

What is the equation for a Linear Absolute Value function?

f(x) = a | x - h | + k

What is the general form of a quadratic equation?

f(x) = ax^2 + bx + c

What is the term for a graph that consists of all integer points?

<p>Discrete</p> Signup and view all the answers

What is the equation for a linear equation?

<p>f(x) = mx + b</p> Signup and view all the answers

What type of graph consists of all real numbers?

<p>Continuous graph</p> Signup and view all the answers

What is the term for a variable that relies on the independent variable?

<p>Dependent</p> Signup and view all the answers

What shape does a quadratic graph take?

<p>U shaped</p> Signup and view all the answers

What shape does a linear absolute value graph take?

<p>V shaped</p> Signup and view all the answers

What is the term for a graph that curves either increasing or decreasing?

<p>Exponential graph</p> Signup and view all the answers

What is the equation for an exponential function?

<p>f(x) = a * b^x</p> Signup and view all the answers

What do real numbers include?

<p>All numbers including decimals and fractions</p> Signup and view all the answers

What are integers?

<p>Counting/whole numbers no decimals or fractions</p> Signup and view all the answers

What describes a straight-line graph that is either increasing or decreasing?

<p>Linear graph</p> Signup and view all the answers

Don't forget this equation in the front if it's a function: f(x) = ______

Signup and view all the answers

Don't forget this equation if it is not a function: x = ______

<h1></h1> Signup and view all the answers

What is the equation of a horizontal line?

<p>f(y) = #</p> Signup and view all the answers

Study Notes

Independent and Dependent Variables

  • An independent variable does not rely on any other variable for its value.
  • A dependent variable relies on the value of the independent variable.

Function Types

  • Linear Absolute Value Function is represented by the equation:
    • f(x) = a |x - h| + k
  • Quadratic Equation is represented by:
    • f(x) = ax² + bx + c
  • Linear Equation is expressed as:
    • f(x) = mx + b
  • Exponential Equation is given by:
    • f(x) = a * b^x

Graph Characteristics

  • Discrete Graphs consist of points that are all integers, plotted separately on the graph.
  • Continuous Graphs feature points that represent all real numbers, forming a connected graph.
  • A U-shaped graph indicates a quadratic relationship.
  • A V-shaped graph represents a linear absolute value relationship.
  • An exponential graph shows a curved line that can either increase or decrease based on the growth factor.

Numerical Classes

  • Real Numbers include all types of numbers, encompassing decimals and fractions.
  • Integers consist of whole numbers without any decimals or fractions.

Important Concepts

  • A linear graph forms a straight line, which can either incline or decline based on the values of its slope.
  • The notation f(x)= indicates that the equation is a function, whereas x=# signifies it is not a function.
  • A horizontal line is represented by the equation:
    • f(y) = #, indicating a constant value of y across all x values.

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Test your knowledge of independent and dependent variables with these flashcards designed for Algebra 1 students. Each card features essential definitions and equations that are fundamental to understanding algebraic concepts.

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