How do you graph #k(x) = ln (x + 3) + 6 #?

1 Answer
Mar 8, 2017

Use the parent function #y = ln(x)# and shift it horizontally #3# to the left (#-3#) and vertically up #6#

Explanation:

The parent function #y = ln(x)# goes through #(1, 0)#:

graph{ln x [-7.04, 12.96, -5.36, 4.64]}

Shift it horizontally #3# to the left #ln(x+3)# so it goes through #(-2, 0)# which is an #x# shift of #-3# from #(1, 0)# :
graph{ln (x+3) [-7.04, 12.96, -5.36, 4.64]}

Shift it vertically up #6#, #ln(x+3) + 6# so #(-2, 0)# moves up to #(-2, 6)#:
graph{ln(x+3) +6 [-4.58, 15.42, -0.64, 9.36]}