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Linear Equations
Domain and Range Domain refers to the x component of a point in the form (x,y). Range refers to the y component of a point in the form (x,y). If you are asked to find the domain of a set of points, simply list the x-values of those points. Likewise, if you are asked to find the range of a set of points, simply list the y-values of those points. Example 1: Find the domain and the range of the following set. {(4,5), (7,8), (-1,3), (3,3), (2,-3)} Domain: Range: {-1, 2, 3, 4, 7} {-3, 3, 5, 8}
What is a Function? An equation or grouping of ordered pairs is a function if and only if no two ordered pairs have the same first coordinate and different second coordinates. Example 2: Example 3: Example 4: Is {(4,5), (2, -4), (1,3)} a function? Yes, it is a function. None of the x-values repeat. Is {(1,-4), (3,5), (3,4), (4, 5)} a function? No, it is not a function. (3,5) and (3,4) have the same x-value. Is {(-1,-2), (2,3), (3,7), (4, 10), (2,3)} a function? Yes, it is. (2,3) is just repeated.
Functional Notation f(x) f(x) is a notation for the naming of functions. The letter f is the name of the function and (x) represents the variable in the function. For example, f(3) means that you should replace the x’s with the number 3. Example 5: Given f(x) = x2 + 5, find f(-2). f(-2) = x2 + 5 f(-2) = (-2)2 + 5 f(-2) = 4 + 5 f(-2) = 9 Evaluate D(e) = 3e - 1, where e = 2. D(2) = 3(2) - 1 D(2) = 6 - 1 D(2) = 5
Example 6:
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Linear Equations
There are two forms that are used with linear equations – standard form and slope-intercept form. It is important to remember that you can switch between the two forms just by algebraically rearranging a problem. Standard Form Ax + By = C This is one of the two forms of a linear equation. The letters A, B, and C represent numbers. The numbers may not be fractions. The most common way to graph an equation in standard form is to find the x and y intercepts. The x and y intercepts are...
Domain and Range Domain refers to the x component of a point in the form (x,y). Range refers to the y component of a point in the form (x,y). If you are asked to find the domain of a set of points, simply list the x-values of those points. Likewise, if you are asked to find the range of a set of points, simply list the y-values of those points. Example 1: Find the domain and the range of the following set. {(4,5), (7,8), (-1,3), (3,3), (2,-3)} Domain: Range: {-1, 2, 3, 4, 7} {-3, 3, 5, 8}
What is a Function? An equation or grouping of ordered pairs is a function if and only if no two ordered pairs have the same first coordinate and different second coordinates. Example 2: Example 3: Example 4: Is {(4,5), (2, -4), (1,3)} a function? Yes, it is a function. None of the x-values repeat. Is {(1,-4), (3,5), (3,4), (4, 5)} a function? No, it is not a function. (3,5) and (3,4) have the same x-value. Is {(-1,-2), (2,3), (3,7), (4, 10), (2,3)} a function? Yes, it is. (2,3) is just repeated.
Functional Notation f(x) f(x) is a notation for the naming of functions. The letter f is the name of the function and (x) represents the variable in the function. For example, f(3) means that you should replace the x’s with the number 3. Example 5: Given f(x) = x2 + 5, find f(-2). f(-2) = x2 + 5 f(-2) = (-2)2 + 5 f(-2) = 4 + 5 f(-2) = 9 Evaluate D(e) = 3e - 1, where e = 2. D(2) = 3(2) - 1 D(2) = 6 - 1 D(2) = 5
Example 6:
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Linear Equations
There are two forms that are used with linear equations – standard form and slope-intercept form. It is important to remember that you can switch between the two forms just by algebraically rearranging a problem. Standard Form Ax + By = C This is one of the two forms of a linear equation. The letters A, B, and C represent numbers. The numbers may not be fractions. The most common way to graph an equation in standard form is to find the x and y intercepts. The x and y intercepts are...