If g(x)=2x + 1, find g(a + h)- g(a). 2h 2h + 2 h + 1

G(x) = 2x + 1

Find g(a + h):
g(a + h) = 2(a + h) + 1 = 2a + 2h + 1

Find g(a):
g(a) = 2(a) + 1 = 2a + 1

Find g(a + h) - g(a):
g(a + h) - g(a) = 2a + 2h + 1 - ( 2a + 1)

Distribute the negative sign:
g(a + h) - g(a) = 2a + 2h + 1 -  2a - 1

Combine like terms:
g(a + h) - g(a) = 2h

2h