The parent graph has been translated 2 units to the right.
Practice makes perfect
To sketch the graph of y=log_5(x-2), we will make necessary transformations to the parent graph of the logarithmic function family with a base of 5.
y=log_5 x
Let's start by sketching this graph. We will also include a few lattice points that fall on the parent graph. Notice that the function has a vertical asymptote at x=0. We will include that as well.
To transform this function, consider the general equation of a logarithmic function with a base of 5.
LOGARITHMIC FUNCTION
y= alog_5(x- h)+ k
[-1em]
&Vertical Stretch: a
&Horizontal Translation: h
&Vertical Translation: k
If we rewrite the given equation to match the same format as above, we can determine all of the transformations that we need to perform.
y= 1log_5(x- 2)+ 0
[-1em]
&Vertical Stretch: 1
&Horizontal Translation: 2
&Vertical Translation: 0
To draw the function, we have to translate it 2 units in the positive horizontal direction. Let's start by translating the vertical asymptote which gives us a point of reference.
By translating the known points the same number of units as the asymptote, we can draw the translated graph.
