Algebra Chapter on Equations and Functions
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Questions and Answers

When is an equation with variables on both sides ready to solve?

When the variables are together and like terms are combined.

Infinite solutions is a true statement.

True

No solution is a false statement.

False

What is mapping in a relation or function?

<p>A visual representation of an input output series.</p> Signup and view all the answers

What is a relation?

<p>A series of input and outputs.</p> Signup and view all the answers

What is a function?

<p>A specific type of relation where each input has only one output.</p> Signup and view all the answers

What is the domain?

<p>Set of all inputs.</p> Signup and view all the answers

What is the range?

<p>Set of all outputs.</p> Signup and view all the answers

What is function notation?

<p>A different way to write a function.</p> Signup and view all the answers

What is absolute maximum?

<p>Highest point on a graph.</p> Signup and view all the answers

What is the y-intercept?

<p>Where the line crosses the Y-axis.</p> Signup and view all the answers

What is absolute minimum?

<p>Lowest point on a graph.</p> Signup and view all the answers

What is relative maximum?

<p>Can't be an endpoint, where it stops going up.</p> Signup and view all the answers

What is relative minimum?

<p>Can't be an endpoint, where it stops going down.</p> Signup and view all the answers

What does the x-axis represent?

<p>Input, domain, independent variable.</p> Signup and view all the answers

What does the y-axis represent?

<p>Output, range, dependent variable.</p> Signup and view all the answers

A continuous graph has points that are connected.

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

A discrete graph has points that are not connected.

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

Growth means that as X increases, Y decreases.

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

Decay means that as X increases, Y decreases.

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

What is slope?

<p>Rise/Run &amp; Y/X.</p> Signup and view all the answers

What is the slope formula?

<p>Y2 - Y1 / X2 - X1.</p> Signup and view all the answers

A negative slope indicates that a line goes up from left to right.

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

A positive slope indicates that a line goes down from left to right.

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

What does slope equal?

<p>Rate of change.</p> Signup and view all the answers

A horizontal line has a slope that is always 0.

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

A vertical line has an undefined slope.

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

What is an explicit formula?

<p>an=a1+d(n-1).</p> Signup and view all the answers

What is a recursive formula?

<p>an=an-1+d.</p> Signup and view all the answers

What is a common difference?

<p>Add or subtract the same amount every time.</p> Signup and view all the answers

What is the linear equations formula?

<p>Ax + By = C.</p> Signup and view all the answers

What is the x-intercept?

<p>Where it crosses the X-axis, Y is zero, the SOLUTION to linear equations, and is also called 0.</p> Signup and view all the answers

What does parallel mean in terms of lines?

<p>Lines that have the same slope but will never intersect.</p> Signup and view all the answers

What does perpendicular mean in terms of lines?

<p>Lines that intersect at 90 degrees, slope is opposite.</p> Signup and view all the answers

What is the slope-intercept form?

<p>Y = mx + b.</p> Signup and view all the answers

What is the point-slope form?

<p>y - y1 = m(x - x1).</p> Signup and view all the answers

What is a one solution system of equations?

<p>Constant &amp; independent.</p> Signup and view all the answers

What is an infinite system of equations?

<p>Constant &amp; dependent.</p> Signup and view all the answers

What is a no solution system of equations?

<p>Inconsistent (parallel).</p> Signup and view all the answers

Study Notes

Equations and Solutions

  • An equation with variables on both sides is ready to solve when there are no parentheses, the variables are combined, and like terms are simplified.
  • Infinite solutions exist when the equation is a true statement for all values.
  • No solution occurs when an equation leads to a false statement.

Functions and Relations

  • Mapping represents a relation or function visually, showcasing the input-output series.
  • A relation consists of a series of input and outputs, while a function is a specific type of relation where each input corresponds to exactly one output.
  • The domain includes all possible inputs, and the range encompasses all possible outputs.

Graphical Concepts

  • Function notation provides an alternative way to express functions.
  • The absolute maximum is the highest point on a graph, while the absolute minimum is the lowest point.
  • Relative maximum and minimum refer to local peaks and valleys, respectively; they cannot be endpoints of a graph.

Axes and Graph Types

  • The x-axis represents the independent variable (inputs, domain) while the y-axis represents the dependent variable (outputs, range).
  • A continuous graph connects all its points, whereas a discrete graph features separate, unconnected points.

Growth and Decay

  • Growth describes a situation where Y increases as X increases.
  • Decay occurs when Y decreases as X increases.

Slope and Lines

  • Slope is calculated using the formula Rise/Run or Y/X.
  • The slope formula is expressed as (Y2 - Y1) / (X2 - X1).
  • A negative slope indicates the line descends from left to right, and a positive slope indicates it ascends.
  • A horizontal line has a slope of 0, while a vertical line has an undefined slope.

Sequences and Formulas

  • An explicit formula is represented as an = a1 + d(n - 1).
  • A recursive formula is expressed as an = an-1 + d.
  • The common difference refers to adding or subtracting the same value repeatedly.

Linear Equations

  • The standard form of a linear equation is Ax + By = C.
  • The x-intercept is the point where the graph crosses the x-axis, resulting in Y being zero.
  • Parallel lines maintain the same slope and never intersect, while perpendicular lines intersect at 90 degrees with opposite slopes.

Forms of Equations

  • Slope-intercept form is given by Y = mx + b, where m is the slope and b is the y-intercept.
  • Point-slope form is expressed as y - y1 = m(x - x1).

Systems of Equations

  • A one-solution system is characterized by being constant and independent.
  • An infinite system arises when the equations are constant and dependent.
  • A no-solution system occurs when the lines are inconsistent, indicating they are parallel.

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Test your understanding of key concepts in algebra, including equations with variables, functions, relations, and graphical representations. This quiz covers infinite and no solutions, function notation, and maximum values. Prepare to apply these concepts in various scenarios.

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