How to Add and Subtract Functions
Write out the functions that are being added or subtracted., Reorder the functions by degree of terms., Create an addition or subtraction problem using the two formulas., Add or subtract like terms., Follow the same process for adding or subtracting...
Step-by-Step Guide
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Step 1: Write out the functions that are being added or subtracted.
Functions are usually stated as f(x) = relationship, where x is the variable input, and the relationship is stated as a formula for the variable x.
Since you are adding or subtracting more than one function, they will be labeled differently, most likely f(x){\displaystyle f(x)} and g(x){\displaystyle g(x)}.
For example, you might be asked to add the function f(x)=3x+2{\displaystyle f(x)=3x+2}, and the function g(x)=4−5x{\displaystyle g(x)=4-5x}.
If you are being asked to add, you will often be asked to find (f+g)x{\displaystyle (f+g)x}.
If you are being asked to subtract, you will often be asked to find (f−g)x{\displaystyle (f-g)x}. -
Step 2: Reorder the functions by degree of terms.
This means ordering the formula by exponents, beginning with the largest exponent (x3,x2,x,{\displaystyle x^{3},x^{2},x,} etc.).
If there is no exponent, order the first-degree term first (x), followed the constants (numbers without variables).
For example, the function g(x){\displaystyle g(x)} would be reordered as −5x+4{\displaystyle
-5x+4}.
The f(x) function is already ordered by degree of terms. , You can add/subtract horizontally or vertically, since you have ordered the functions by terms.
For example, your function can be set up as (f+g)x=(3x+2)+(−5x+4){\displaystyle (f+g)x=(3x+2)+(-5x+4)}, or it could be set up vertically, with like terms lined up:+3x+2−5x+4{\displaystyle +{\begin{matrix}3x&+&2\\-5x&+&4\end{matrix}}}. , It is helpful to add/subtract in order of the degree of terms, beginning with the highest exponent (if any).
For example, for (f+g)x=(3x+2)+(−5x+4){\displaystyle (f+g)x=(3x+2)+(-5x+4)}, you would first add the first-degree terms:3x+(−5x)=−2x{\displaystyle 3x+(-5x)=-2x}.Second, you would add the constants:2+4=6{\displaystyle 2+4=6}.So (f+g)x=−2x+6{\displaystyle (f+g)x=-2x+6}. , Adding or subtracting functions is always just a matter of adding/subtracting the like terms in the relationship formulas. -
Step 3: Create an addition or subtraction problem using the two formulas.
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Step 4: Add or subtract like terms.
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Step 5: Follow the same process for adding or subtracting more than two functions.
Detailed Guide
Functions are usually stated as f(x) = relationship, where x is the variable input, and the relationship is stated as a formula for the variable x.
Since you are adding or subtracting more than one function, they will be labeled differently, most likely f(x){\displaystyle f(x)} and g(x){\displaystyle g(x)}.
For example, you might be asked to add the function f(x)=3x+2{\displaystyle f(x)=3x+2}, and the function g(x)=4−5x{\displaystyle g(x)=4-5x}.
If you are being asked to add, you will often be asked to find (f+g)x{\displaystyle (f+g)x}.
If you are being asked to subtract, you will often be asked to find (f−g)x{\displaystyle (f-g)x}.
This means ordering the formula by exponents, beginning with the largest exponent (x3,x2,x,{\displaystyle x^{3},x^{2},x,} etc.).
If there is no exponent, order the first-degree term first (x), followed the constants (numbers without variables).
For example, the function g(x){\displaystyle g(x)} would be reordered as −5x+4{\displaystyle
-5x+4}.
The f(x) function is already ordered by degree of terms. , You can add/subtract horizontally or vertically, since you have ordered the functions by terms.
For example, your function can be set up as (f+g)x=(3x+2)+(−5x+4){\displaystyle (f+g)x=(3x+2)+(-5x+4)}, or it could be set up vertically, with like terms lined up:+3x+2−5x+4{\displaystyle +{\begin{matrix}3x&+&2\\-5x&+&4\end{matrix}}}. , It is helpful to add/subtract in order of the degree of terms, beginning with the highest exponent (if any).
For example, for (f+g)x=(3x+2)+(−5x+4){\displaystyle (f+g)x=(3x+2)+(-5x+4)}, you would first add the first-degree terms:3x+(−5x)=−2x{\displaystyle 3x+(-5x)=-2x}.Second, you would add the constants:2+4=6{\displaystyle 2+4=6}.So (f+g)x=−2x+6{\displaystyle (f+g)x=-2x+6}. , Adding or subtracting functions is always just a matter of adding/subtracting the like terms in the relationship formulas.
About the Author
Larry Burns
Writer and educator with a focus on practical creative arts knowledge.
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