# To evaluate f ( x ) = 3 x + 2 at a number, substitute the number for x in the definition of f ( x ) The given function of the values f ( a ) = 3 a + 2 , f ( a + h ) = 3 a + 3 h + 2 , f ( a + h ) − f ( a ) h = 3 Given information: consider the function f ( x ) = 6 x − 18 Calculation: Start by assume x is the variable of a function f ( x ) . Evaluate the values of the function f ( x ) = 3 x + 2 for the given values of the variable x Plug the value x = a , in the function f ( x ) = 3 x + 2 then the value of f ( a ) . f ( a ) = 3 a + 2 Plug the value x = a + h , in the function f ( x ) = 3 x + 2 then the value of f ( a + h ) . f ( a + h ) = 3 ( a + h ) + 2 f ( a + h ) = 3 a + 3 h + 2 f ( a + h ) − f ( a ) h = 3 a + 3 h + 2 − ( 3 a + 2 ) h Since f ( a ) = 3 a + 2 , f ( a + h ) = 3 a + 3 h + 2 = 3 a + 3 h + 2 − 3 a − 2 h = 3 h h = 3 Thus, f ( a ) = 3 a + 2 , f ( a + h ) = 3 a + 3 h + 2 , f ( a + h ) − f ( a ) h = 3 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.1, Problem 35E
Solution

## To evaluate f(x)=3x+2 at a number, substitute the number for x in the definition of f(x)The given function of the values f(a)=3a+2,f(a+h)=3a+3h+2,f(a+h)−f(a)h=3Given information:consider the function f(x)=6x−18Calculation:Start by assume x is the variable of a function f(x) .Evaluate the values of the function f(x)=3x+2 for the given values of the variable xPlug the value x=a, in the function f(x)=3x+2 then the value of f(a).  f(a)=3a+2Plug the value x=a+h, in the function f(x)=3x+2 then the value of f(a+h).  f(a+h)=3(a+h)+2f(a+h)=3a+3h+2  f(a+h)−f(a)h=3a+3h+2−(3a+2)h        Since f(a)=3a+2,f(a+h)=3a+3h+2=3a+3h+2−3a−2h=3hh=3Thus, f(a)=3a+2,f(a+h)=3a+3h+2,f(a+h)−f(a)h=3

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