State the domain and range of the relation shown in the graph. Is the relation a function? You try: A relation is represented by
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1 1 State the domain and range of the relation shown in the graph. Is the relation a function? 1a A relation is represented by! Remember: A relation is a set of ordered pairs that can be represented by a diagram, graph, or sentence. The set of all first numbers of the ordered pairs in a relation is called the domain of the relation. The set of all second numbers of the ordered pairs in a relation is called range of the relation. A relation in which every domain has only one range value is called a function. 1b Selected Response. Select each relation below that is a function. Key Note y If no vertical line intersects a graph in more than one point, the graph represents a function. x F.IF.1 F.IF.1 Page 1 of 12 MCC@WCCUSD 01/12/2015
2 ( ) = x 2 + 4x 3 2 Consider f x A. Find the y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex. The function is of the form so we can identify a, b, and c. 2 Continued C. Use the information to graph the function. Graph the points from the table and connect them with a smooth curve. Draw the axis of symmetry, as a dashed line. The graph should be symmetrical about this line. Use a and b to find the equation of the axis of symmetry. The equation of the axis of symmetry is Therefore the x-coordinate of the vertex is B. Make a table of values that includes the vertex. Select five specific points, with the vertex in the middle and two points on either side of the vertex, including the y-intercept and its reflection. Use symmetry to determine the y- values of the reflection. D. Determine whether the function has a maximum or minimum value and find that value. State the domain and range of the function. For this function,, so the graph opens up and has a minimum value. vertex F.IF.4 Page 2 of 12 MCC@WCCUSD 01/12/2015
3 2a Complete parts A-D for the quadratic function below. A. Find the y-intercept, the equation of the axis of symmetry and the x-coordinate of the vertex. 2a Continued D. Determine whether the function has a maximum or minimum value, and find that value. State the domain and range of the function. B. Make a table of values that includes the vertex. F.IF.4 2b Two functions are shown below. C. Use this information to graph the function. Select all that are true about F.IF.4 Page 3 of 12 MCC@WCCUSD 01/12/2015
4 3 Write the piecewise-defined function shown in the graph below. 3a Write the piecewise-defined function shown in the graph below. F.IF.4, F.IF.7.b Remember: In graphing a piecewise-defined function, pieces may or may not connect. 3b Select all of the following that are true about the graph below. Examine and write a function for each portion of the graph. Write the piecewise-defined function. F.IF.4, F.IF.7.b F.IF.4, F.IF.7.b Page 4 of 12 MCC@WCCUSD 01/12/2015
5 4 4 Continued Step 4: The rate of change from one point to the next can be found using the slope formula. Complete the table for all the y-values. Step 5: The second-order difference can be found by subtracting consecutive first-order differences. F.IF.6 Page 5 of 12 MCC@WCCUSD 01/12/2015
6 4 4 Continued Make a table of values for the given x-values. Graph the function. Then determine the firstorder and second-order differences. x Step 4: Find the rate of change using the slope formula. Step 5: Complete the table. Find up to the secondorder difference. F.IF.6 Page 6 of 12 MCC@WCCUSD 01/12/2015
7 5 Let be any two function. You can add, subtract, multiply and divide functions according to these rules. 5 Continued Sum Operation Definition Difference Product Quotient Function of a function Ex: Given Find each function. F.BF.1.b, F.IF.9 5 F.BF.1.a, F.IF.9 F.BF.1.a, F.IF.9 Page 7 of 12 MCC@WCCUSD 01/12/2015
8 6 The inverse of the exponential function is the logarithmic function This function is usually written as and is read y equals log base b of x. 6 Match each logarithmic equation to its exponential form(s) in the box. Ex # 1: Write each logarithmic equation to exponential form. Ex # 2: Write each exponential equation to logarithmic form. Ex # 3: Evaluate F.BF.3, F.IF.7e End of Study Guide Ex # 4: Solve F.BF.3, F.IF.7e Page 8 of 12 MCC@WCCUSD 01/12/2015
9 1 You Try Solutions: A relation is represented by 2 Complete parts A-D for the quadratic function below. A. Find the y-intercept, the equation of the axis of symmetry and the x-coordinate of the vertex. The function is of the form so we can identify a, b, and c. Use a and b to find the equation of the axis of symmetry.! B. Make a table of values that includes the vertex. x f(x) (x, f(x)) 0 5 (0, 5) 1-1 (1, -1) 2-3 (2, -3) 3-1 (3, -1) 4 5 (4, 5) 1b Selected Response Answers Select all that apply The vertex is. F.IF.1 F.IF.4 Page 9 of 12 MCC@WCCUSD 01/12/2015
10 continued # 2a C. Use this information to graph the function. 3a Write the piecewise-defined function shown in the graph below. D. Determine whether the function has a maximum or minimum value, and find that value. State the domain and range of the function. For the function, so the graph opens up and the function has a minimum value of. The domain is all real numbers. The range is all real number greater than or equal to the minimum F.IF.4 F.IF.4, F.IF.7.b 2b Selected Response Answer: 3b You Try Selected Response Answer: Select all that apply Select all that apply F.IF.4 F.IF.4, F.IF.7.b Page 10 of 12 MCC@WCCUSD 01/12/2015
11 4 4 Continued Make a table of values for the given x-values. Graph the function. Then determine the firstorder and second-order differences. Step 4: The rate of change from one point to the next can be found using the slope formula. Step 5: The second-order difference can be found by subtracting consecutive first-order difference. F.IF.6 F.IF.6 Page 11 of 12 MCC@WCCUSD 01/12/2015
12 5 You Try 6 Match each logarithmic equation to its exponential form(s) in the box. Selected Response Answer: Select all that apply Answer: F.BF.1.a, F.IF.9 F.BF.3, F.IF.7e End of Study Guide Page 12 of 12 MCC@WCCUSD 01/12/2015
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