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Lesson 1-3, 1-4 Represent Functions as Graphs; Graphing Linear Equations using Intercepts. Graph a function Graph the function y=3x with domain 0,1,2,3,4. Step 1: Make an input-output table. X 0 1 2 3 4 y 0 3 6 9 12 Step 2: Plot a point for each ordered pair. Practice Problems Graph the functions: 1) y=2x+3 Domain: 0,2,4,6,8 2) y=-2x-7 Domain: 1,2,3,4,5 3) y=-3/4x+6 Domain: 0,4,8,12,16 4) y= y=1/2x-4 Domain: 1,2,3,4,5 5) y=1/3x-3 Domain: 0,3,6,9,12 Write a function rule for a graph. See Graph Step 1: Make a table Step 2: Find a relationship between the inputs and outputs. Step 3: Write a function rule. Helpful Hints to Writing Rules First, check for a common DIFFERENCE between x and y values. For example, x 1 3 4 7 y 3 5 6 9 •The DIFFERENCE of every value of x and y is 2. Therefore, the rule is y=x+2. Helpful Hints to Writing Rules Second, if no common difference is found, check for a COMMON MULTIPLIER. For example, x 1 2 3 4 y 4 8 12 16 •Every value of x can be multiplied by 4 to get the values for y. Therefore, the rule is y=4x. Helpful Hints for Writing Rules If no common difference or multiplier can be found, check for BOTH! For example, x 1 2 3 4 y 4 7 10 13 •In the table above, there is no common difference between x and y. 4-1=3 but 7-2=5. Also, there is no common multiplier. 1x4=4, but 2x4≠7. Therefore, we check for BOTH, 1x3=3, then, 3+1=4. 3x3=9, then, 9+1=10. So, the rule is y=3x+1. Lesson 1-4 Graph Using Intercepts Find x-intercept and y-intercept of the graph of 7x3y=21 Solution: To find x-intercept, sub 0 for y and solve for x. 7x-3y=21 7x-3(0)=21 x=21/7 or x=3 To find y-intercept, sub 0 for x and solve for y. 7x-3y=21 7(0)-3y=21 y=-21/3 or -7 Use a Graph to find Intercepts Find the x and y intercepts of the graph. (2,0) (0,-4) The line crosses the x-axis at 2, therefore the x-intercept is 2. The line crosses the y-axis at -4, therefore the y-intercept is -4. Use Intercepts to Graph an Equation Graph 3x+2y=6. Label the points where the line crossed the axes. Step 1: Find the intercepts. x-intercept 3x+2y=6 3(0)+2y=6 y=3 y-intercept Step 2: Plot the points on a graph. 3x+2y=6 3x+2(0)=6 x=2 X-int= (2,0) Y-int= (0,3) Step 3: Connect the points with a line. (0,3) (2,0) Guided Practice Pg. 18 Problems 1-5 Assignment pg. 19 1-27 (odd only)