How do you graph #Y= log ( x + 1 ) - 7#?

1 Answer
Dec 20, 2017

Answer:

See explanation.

Explanation:

Start by knowing the graph of #y=log(x)#. It's three key features are its shape, #x#-intercept at #(1,0)#, and vertical asymptote at #x=0#.

Now we take each transformation one at a time and see what happens.

The #x+1# causes the graph to shift 1 unit to the left, changing the location of the asymptote to #x=-1# and changing the #x#-intercept to #(0,0)#.

Now shift this new graph 7 units down because of the #-7#. This doesn't change the asymptote but takes the point that was the #x#-intercept and moves it to #(0,-7)#.

None of these changes alter the shape of the graph (they're rigid transformations). So our new graph has exactly the same shape, a key point at #(0,-7)#, and a vertical asymptote at #x=-1#.