| Linear Functions and Graphs |
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| 1) Define a relation. |
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| 2) Define a function. |
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| 3) Define domain. |
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| 4) Define range. |
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| In the following problems, describe the domain and the range of each relation. Determine if the relation is a function. Explain your reasoning. |
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5) What is the domain and range? Is the relation a function? Explain why or why not.
{(8.4, 3.8), (6.5, –2.6), (–3, 6)} |
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6) What is the domain and range? Is the relation a function? Explain why or why not.
{(2, 0), (5, 0), (0, 5), (0, 2)} |
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7) What is the domain and range? Is the relation a function? Explain why or why not.
{(7, 1), (7, 200)} |
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8) What is the domain and range? Is the relation a function? Explain why or why not.
{(–1, –1), (2, 2), (4, 4), (–7, –7)} |
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| Use the following scenario to answer the next three questions: The Crum’s are renting a car for a vacation in San Antonio, Texas. The cost is $16 per day and a onetime fee of $25.00. |
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| 11) Fill in the missing information for the domain and range in the chart below. State the letter, and then the answer for each missing part. |
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| 12) Which number would not be an acceptable domain value? |
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13) Which of the following equations would correctly represent the data in the completed chart?
(Note: When each of the domain values are substituted for x, the result will be the corresponding y-value.) |
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In the following problems, complete each ordered pair so that it is a solution to –2x + y = 3.
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| 15) Find the x-coordinate of the point (?, –4) that makes it a solution to the equation, –2x + y = 3? |
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| 16) What is the x-coordinate of the point (?, 0) that makes it a solution to the equation, –2x + y = 3? |
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| Extra Practice: Check with you instructor to see if s/he would like for you to do some extra practice problems. Click here to view the practice worksheet. |
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| 18) Describe the steps in determining the slope of a line that is graphed on a coordinate plane. |
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| In the following questions, determine the slope of the line graphed. |
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| 23) Describe the slopes of lines with positive slopes. |
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| 24) Describe the slopes of lines with negative slopes. |
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| Extra Practice: Check with you instructor to see if s/he would like for you to do some extra practice problems. Click here to view the practice worksheet. |
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| 26) Describe how to find the slope of a line using two points. |
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| In the following problems, find the slope of the line that contains each pair of points. |
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| Extra Practice: Check with you instructor to see if s/he would like for you to do some extra practice problems. Click here to view the practice worksheet. |
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| Graphing a Line on a Coordinate Plane Using a Point and the Slope |
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| 30) Describe how to graph a linear equation given the slope and a point on the line. |
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| For the next three questions, draw a line on graph paper that has the given slope and contains the given point. Determine which graph is correct. |
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| 31) Which graph is correct for the line that contains the given point and has the given slope? |
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32) Which graph is correct for the line that contains the following point and has the given slope? (0, 0), m = 3
(Hint: 3 = 3/1) |
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| 33) Which graph is correct for the line that contains the following point and has the given slope? (3, –2), undefined slope |
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| 34) The graph provides data points that can be used to determine the traveling rate from Pittsburgh (PA) to New York City. What is the average rate of change (in this case, miles per hour) of the train? Express the rate rounded to the nearest tenth. |
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| Brenton received a pay raise and the chart below represents his current earnings. Use this chart to answer the following questions. |
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| 35) Does the data in the chart represent a function? Explain why or why not. |
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| 36) What is the rate of change when comparing wages earned to the hours Brenton worked? Explain what the rate of change means to Brenton in terms of money? |
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| 37) Tommy takes his dog Em for a walk after school. Which scenario is represented best by the graph in terms of Tommy and Em's walk and rate of change? |
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| 38) Describe a real-life example which illustrates direct variation between values of numbers. |
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In the following problems, “y varies directly as x.” Determine and state the constant of variation, and then write an equation of direct variation for the given x and y values.
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44) Simplify.
Click here to review the unit content explanation for Rational Numbers and Exponents. |
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| 46) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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| No offline activities found |
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