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Questions and Answers

What does this arrow diagram represent?

The relation between a word and the number of letters in the word.

Represent this relation in two different ways.

  • As a set of ordered pairs and as a table. (correct)
  • As a graph and as a set of ordered pairs. (correct)
  • As a graph and as a table.
  • As a graph, as a set of ordered pairs, and as a table.

List the set of ordered pairs of the form: (digit, number of segments lit up)

(0, 6), (1, 2), (2, 5), (3, 5), (4, 4),(5, 5), (6, 6), (7, 3), (8, 7), (9, 6)

How many children are shown?

<p>6</p> Signup and view all the answers

How many parents are shown?

<p>4</p> Signup and view all the answers

Which sets of ordered pairs represent functions? Identify the domain and range of each set of ordered pairs.

<p>{(2, 3), (4, 5), (6, 7), (8, 9)} Domain: {2, 4, 6, 8} Range: {3, 5, 7, 9} (A), {(1, 3), (2, 6), (3, 9), (4, 12)} Domain: {1, 2, 3, 4} Range: {3, 6, 9, 12} (C)</p> Signup and view all the answers

Which statement is true? Give an example to justify your choice.

<p>All functions are relations, but not all relations are functions. For example, the relation {(1, 2), (2, 3), (1, 4)} is not a function because the input value 1 has two different output values. (A)</p> Signup and view all the answers

Create two different tables to represent relations that associate these letters and their points.

<p>Table 1:</p> <table> <thead> <tr> <th>Letter</th> <th>Points</th> </tr> </thead> <tbody> <tr> <td>A</td> <td>2</td> </tr> <tr> <td>D</td> <td>2</td> </tr> <tr> <td>F</td> <td>2</td> </tr> <tr> <td>G</td> <td>2</td> </tr> <tr> <td>M</td> <td>3</td> </tr> <tr> <td>Q</td> <td>10</td> </tr> <tr> <td>T</td> <td>1</td> </tr> <tr> <td>X</td> <td>10</td> </tr> <tr> <td>Z</td> <td>10</td> </tr> </tbody> </table> <p>Table 2:</p> <table> <thead> <tr> <th>Points</th> <th>Letters</th> </tr> </thead> <tbody> <tr> <td>2</td> <td>A, D, F, G</td> </tr> <tr> <td>3</td> <td>M</td> </tr> <tr> <td>10</td> <td>Q, T, X, Z</td> </tr> </tbody> </table> Signup and view all the answers

Which table in part a represents a function? Justify your choice.

<p>Table 2, because each letter has only one point. (C)</p> Signup and view all the answers

For the function f(x)=−5x+11, determine: f(1)

<p>6</p> Signup and view all the answers

For the function f(n)=2n−7, determine n when: f(n)=11

<p>9</p> Signup and view all the answers

For the function g(x)=−5x+1, determine x when: g(x)=41

<p>-8</p> Signup and view all the answers

The lengths of the sides of a triangle, in units, are s, s+5, and t. Its perimeter is 16 units. Use function notation to express t as a function of s. What are the domain and range of the function?

<p>t(s) = 11 − 2s; domain: 1.5 &lt; s &lt; 3, range: 5 &lt; t &lt; 8</p> Signup and view all the answers

Which of these graphs represent a function? Justify your answer.

<p>Graph c. Each vertical line intersects the graph at most once. (A), Graph a. Each vertical line intersects the graph at most once. (C), Graph e. Each vertical line intersects the graph at most once. (D)</p> Signup and view all the answers

Determine the domain and range of the graph of each function.

<p>a) Domain : The x-values of the graph are all real numbers (from -2 to 4). Range : The y-values of the graph range from -2 to 4. b) Domain : The x-values of the graph are all real numbers (from -2 to 4). Range : The y-values of the graph range from -2 to 4. c) Domain : The x-values of the graph range from -2 to 4. Range: The y-values of the graph remain constant at y =2. d) Domain : The x-values of the graph range from -2 to 4. Range: The y-values of the graph are all real numbers.</p> Signup and view all the answers

Is this a function? Find f(-1) and find f(2).

<p>Yes, it is a function. f(-1) = -1 and f(2) = -5 (C)</p> Signup and view all the answers

Explain why this graph represents a function

<p>Each vertical line intersects the graph at most once.</p> Signup and view all the answers

Find f(-1)

<p>-1</p> Signup and view all the answers

State the domain and range for this function.

<p>Domain: all real numbers; Range: -6 ≤ y ≤ 4</p> Signup and view all the answers

Flashcards

Function

A relation where each input value has only one output value.

Domain

The set of all possible input values (x-values) in a relation or function.

Range

The set of all possible output values (y-values) in a relation or function.

Linear Function

A function whose graph is a straight line.

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Function Notation

A way to represent a function, using f(x) to denote the output for input x.

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f(1)

The value of the function f at x = 1.

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Slope

The rate of change of a linear function, represented by 'm'.

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x-intercept

The point where a graph crosses the x-axis.

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y-intercept

The point where a graph crosses the y-axis.

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Midpoint

The point that is exactly halfway between two given points.

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Distance

The length between two points in a coordinate plane.

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Parallel Lines

Lines that have the same slope.

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Perpendicular Lines

Lines that intersect at a 90-degree angle.

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Standard Form

A way to express the equation of a line: Ax + By = C.

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Slope-intercept Form

A way to express the equation of a line: y = mx + b.

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Point-slope Form

A way to express the equation of a line using a point and slope.

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Circle

A set of points equidistant from a center point.

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Ellipse

A set of points where the sum distances to two fixed points (foci) is constant.

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Domain of a Graph

The set of all x-values on a graph.

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Range of a Graph

The set of all y-values on a graph.

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Linear Relation

A relation whose graph is a straight line.

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