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Let's take a look at some equations, using two variables,
which can be used to express functions.
Functions such as: y = 3x + 10 (linear) or y = x2 + 4 (non-linear)
The two variables are x and y, where x is the independent variable.
Functions represent the "relationships between variables".
Things to keep in mind:
• Not ALL equations are functions (consider x + 2 = 8 : it has only 1 variable)
• Not ALL functions are represented as equations (some functions are represented in a table or as a graphical display). |
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1. |
Given the equation 2x + y = 15. Write the equation in "y =" form.
Solution: We need to solve this equation for y, so that an expression with x remains.
2x + y = 15
y = -2x + 15
In "y =" form we have y = -2x + 15.
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2. |
Given a function represented by the equation ½ y + ¾ x = 4. Write the equation equation in "y =" form.
Solution: We need to solve this equation for y, so that an expression with x remains.
½ y + ¾ x = 4
½ y = 4 - ¾ x
y = 8 - 1½ x
In "y =" form we have y = 8 - 1½ x.
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3. |
Given an input value of x, the function outputs a value y to satisfy the equation 2y + 4x = 82. Write the equation in "y =" form.
Solution: Solve the equation for y, so that an expression with x remains.
2y + 4x = 82
2y = -4x + 82
y = -2x + 41
In "y =" form we have y = -2x + 41.
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In plain English ...
... equations for functions are generally expressed in "y =" form. Most graphing calculators graph only functions, where the equation is entered in a "y =" location on the calculator. |
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