The parent function is the simplest function in a family of functions.
B
b
The asymptote is a vertical line.
C
c
To translate something horizontally, we have to add or subtract from x. Also, use the one lattice point on the graph to determine the base.
A
a
y=log x
B
b
x=2
C
c
y=log_2(x-2)
Practice makes perfect
a
The parent function is the simplest function within a family of functions. Examining the graph we see that it is a logarithmic function, and therefore the parent function is y=log x.
When we add or subtract a constant to a function's input, the resulting transformation is a horizontal translation to the left and right respectively. In this case, we want a horizontal translation to the right by 2 units. This means we have to subtract 2 from x.
To determine the base of the logarithm, we can use the one lattice point on the graph.
Let's substitute the known point on the graph into our function.
2=log_b(6-2) ⇔ 2=log_b 4
Using the definition of a logarithm, we can rewrite the equation.
2=log_b 4 ⇔ b^2= 4
Let's solve for b. Notice that the base of a logarithm can only be positive.
