Relations and Functions Quiz
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Questions and Answers

What is a relation?

Set of ordered pairs.

What is an ordered pair?

The x and y coordinates of a point on the coordinate plane (x,y).

What is a coordinate plane?

A plane formed by 2 perpendicular lines called axes.

What is a function?

<p>A special relation where each x-value is paired with ONLY ONE y-value.</p> Signup and view all the answers

What is a mapping?

<p>Bubbles that represent the x-values and the y-values.</p> Signup and view all the answers

What is a table in terms of ordered pairs?

<p>A way to represent ordered pairs.</p> Signup and view all the answers

What is the domain?

<p>Set of all the possible x-values.</p> Signup and view all the answers

What is the range?

<p>Set of all the possible y-values.</p> Signup and view all the answers

What is an independent variable?

<p>The INPUT or CAUSE in a situation or problem.</p> Signup and view all the answers

What is a dependent variable?

<p>The OUTPUT or RESULT in a situation or problem.</p> Signup and view all the answers

What are other names for 'x'?

<p>Domain, independent variable, input.</p> Signup and view all the answers

What are other names for 'y'?

<p>f(x), range, dependent variable, output.</p> Signup and view all the answers

What is the vertical line test?

<p>A relation is a function if a vertical line touches the graph only ONE time.</p> Signup and view all the answers

What is a discrete function?

<p>Data appears as individual points on a graph.</p> Signup and view all the answers

What is a continuous function?

<p>Data appears as a smooth curve on a graph.</p> Signup and view all the answers

In the equation y = mx + b, what does 'm' stand for?

<p>Slope.</p> Signup and view all the answers

In the equation y = mx + b, what does 'b' stand for?

<p>The y-intercept.</p> Signup and view all the answers

What happens when you change the 'm' in the slope-intercept form of a line?

<p>It changes the steepness of the line.</p> Signup and view all the answers

What happens when you change the 'b' in the slope-intercept form of a line?

<p>It moves the line up or down the y-axis.</p> Signup and view all the answers

Define slope.

<p>The steepness of a line, vertical change/horizontal change.</p> Signup and view all the answers

What slope does a horizontal line have?

<p>Slope = 0.</p> Signup and view all the answers

What slope does a vertical line have?

<p>Undefined slope.</p> Signup and view all the answers

What is the x-intercept?

<p>The point where the graph crosses the x-axis.</p> Signup and view all the answers

What is the y-intercept?

<p>The point where the graph crosses the y-axis.</p> Signup and view all the answers

What is a linear inequality?

<p>An equation with &lt; or =, &gt; or = in place of the =.</p> Signup and view all the answers

How do you combine like terms?

<p>Add their coefficients.</p> Signup and view all the answers

What is the 'rate of change' on a graph?

<p>Slope.</p> Signup and view all the answers

What is the range in terms of data sets?

<p>Subtract the smallest from the largest.</p> Signup and view all the answers

When do you use a solid line and closed circle?

<p>If it has the line under it (or equal to).</p> Signup and view all the answers

Solve the literal equation R = A - P/T.

<p>R = A - P/T.</p> Signup and view all the answers

When do you flip an inequality symbol?

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

Are y= and f(x)= the same?

<p>Yes.</p> Signup and view all the answers

How to solve function notation?

<p>Replace the x with a given value and solve.</p> Signup and view all the answers

What is another name for slope?

<p>Rate of change.</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 - y*) = m (x - x*).</p> Signup and view all the answers

What is the standard form of a line?

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

Study Notes

Relations and Functions

  • A relation consists of a set of ordered pairs.
  • An ordered pair represents the coordinates of a point in the format (x, y).
  • The coordinate plane is defined by two perpendicular axes: the x-axis (horizontal) and y-axis (vertical).
  • A function is a specific type of relation where each x-value corresponds to only one y-value, ensuring no x-values repeat; verified through the vertical line test.

Variables and Terminology

  • The domain includes all possible x-values (inputs).
  • The range includes all potential y-values (outputs).
  • The independent variable (x) represents the input or cause, while the dependent variable (y) illustrates the output or result.
  • Other terms for x include domain, independent variable, and input. Alternative terms for y include f(x), range, dependent variable, and output.

Graphing and Slope

  • Use the vertical line test to determine if a relation is a function: a vertical line must intersect the graph once.
  • A discrete function is depicted as separate points on a graph, while a continuous function appears as a smooth curve.
  • The slope measures a line's steepness, calculated as vertical change/horizontal change (rise over run); it can also indicate the rate of change.

Line Characteristics

  • In the equation y = mx + b:
    • "m" denotes the slope.
    • "b" indicates the y-intercept.
  • Changing "m" alters the line's steepness, while altering "b" moves the line up or down the y-axis.
  • A horizontal line has a slope of 0; a vertical line has an undefined slope.

Intercepts and Inequalities

  • The x-intercept is where the graph crosses the x-axis, with coordinates (x, 0).
  • The y-intercept is where the graph crosses the y-axis, with coordinates (0, y).
  • A linear inequality contains inequalities (<, >, ≤, or ≥) instead of an equation.

Combining Terms and Solving

  • Combine like terms by adding their coefficients.
  • For inequalities, flip the inequality symbol when multiplying or dividing by a negative number.
  • When solving in function notation, substitute the x-value in the function and solve accordingly.

Equation Forms

  • Slope-intercept form of a line: y = mx + b.
  • Point-slope form: (y - y) = m (x - x)**; used to graph when both slope and a point are known.
  • The standard form of a line is given by Ax + By = C, requiring no fractions or decimals, with A being positive.

Additional Concepts

  • Rate of Change is synonymous with slope and is often referenced in word problems.
  • When determining range from a data set, order values from smallest to largest and subtract the smallest from the largest to find the range.

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Description

Test your knowledge of relations and functions with this quiz. You'll explore concepts like ordered pairs, domain, and range, as well as the distinction between independent and dependent variables. Challenge yourself to apply the vertical line test and understand how to graph these mathematical principles.

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