# Function

Written by Jerry Ratzlaff on . Posted in Algebra

Function is a relationship where a set of inputs (domain) determine a set of possible outputs (range).  The function of  $$\large{ f \left( x \right) = 5\;x }$$  is  $$\large{ f \left( x \right) }$$ , the function name is  $$\large{ f }$$ , the input value is  $$\large{ \left( x \right) }$$ , and the output is  $$\large{ 5\;x }$$ .

• $$\large{\; f \left( x \right) = 5\;x }$$ , find  $$\large{ f \left( 2 \right) }$$
• $$\large{\; f \left( 2 \right) = 5\left( 2 \right) = 10 }$$

• $$\large{\; f \left( x \right) = 5x + 3x^2 - 4 + 3 }$$ , find  $$\large{ f \left( 2y + 5 \right) }$$
• $$\large{\; f \left( 2y + 5 \right) = 5\left( 2y + 5 \right) + 3\left( 2y + 5 \right)^2 - 4 + 3 }$$
• $$\large{\; = 10y + 25 + 3\left( 4y^2 + 12y + 25 \right) - 4 + 3 }$$
• $$\large{\; = 10y + 25 + 12y^2 + 36y + 75 - 4 + 3 }$$
• $$\large{\; = 46y + 99 + 12y^2 }$$