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# Evaluate Functions Help

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By McGraw-Hill Professional
Updated on Oct 4, 2011

## Introduction to Evaluating Functions

Functions can be evaluated at quantities that are not numbers, but the idea is the same—substitute the quantity in the parentheses for x and simplify.

#### Examples

• Evaluate f ( a + 3), f ( a 2 ), f ( u − v ), and f ( a + h) for f ( x ) = 8 x + 5. We will let x = a + 3, x = a 2 , x = u − v , and x = a + h in the function.

f ( a + 3) = 8( a + 3) + 5 = 8 a + 24 + 5 = 8 a + 29

f ( a 2 ) = 8( a 2 ) + 5 = 8 a 2 + 5

f ( u − v ) = 8( uv ) + 5 = 8 u − 8 v + 5

f ( a + h ) = 8( a + h ) + 5 = 8 a + 8 h + 5

• Evaluate f (10 a ), f (− a ), f ( a + h ), and f ( x + 1) for f ( x ) = x 2 + 3 x − 4.

f (10a) = (10 a ) 2 + 3(10 a ) − 4 = 10 2 a 2 + 30 a − 4 = 100 a 2 + 30 a − 4

f (− a ) = (− a ) 2 + 3(−a) − 4 = a 2 − 3 a − 4

Remember, (− a ) 2 = (− a )(− a ) = a 2 , not − a 2 .

f ( a + h) = ( a + h ) 2 + 3( a + h ) − 4 = ( a + h )( a + h ) + 3( a + h ) − 4

= a 2 + 2 ah + h 2 + 3 a + 3 h −4

f ( x + 1) = ( x + 1) 2 + 3( x + 1) − 4 = ( x + 1)( x + 1) + 3( x + 1) − 4

= x 2 + 2 x + 1 + 3 x + 3 − 4 = x 2 + 5 x

• Find f ( a − 12), f ( a 2 + 1), f ( a + h ), and f ( x + 3) for f ( x ) = −4. This is a constant function, so the y -value is −4 no matter what is in the parentheses.
• f ( a − 12) = −4     f ( a 2 + 1) = −4

f ( a + h ) = −4     f ( x + 3) = −4

• Find f (2 u + v ), , and f (2 x ) for

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