Find and simplify each of the following for ​f(x)=7x−5

Question

Find and simplify each of the following for ​f(x)=7x−5

​(A) f(x+h)

​(B) f(x+h)−f(x)

​(C) f(x+h)−f(x) / h

​(A) f(x+h) = _________ ​(Do not​ factor.)

Answer 1

A) Evaluate the function at f(x+h)

1. f(x+h)=7(x+h)-5 (Distribute the 7 inside the parentheses)
2. f(x+h)=7x+7h-5

B) f(x+h)-f(x) See the A) for f(x+h)

1. f(x+h)-f(x)=(7x+7h-5)-(7x-5) (Distribute the negative sign to f(x)
2. f(x+h)-f(x)=7x+7h-5-7x+5 (Combine like terms, 7x-7x, -5+5)
3. f(x+h)-f(x)=7h

C)f(x+h)−f(x) / h= See B) for numerator

1. f(x+h)−f(x) / h=7h/h (cancel the h terms)
2. f(x+h)−f(x) / h=7