Question

In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achieve the graph of g(x) = log(-3x-6) - 2.

Answer 1

log(2x)=4

log2⁢x=4 in exponential form using the definition of a logarithm. If

x x and b b are positive real numbers and b ≠ 1, then log b(x)=y logbx=y is equivalent to by=x. 10 4 = 2x

hope it helps

Answer 2

Answer and explanation:

Given : The transformation(s) that take place on the parent function $f(x) = \log(x)$ to achieve the graph of $g(x) = \log(-3x-6) - 2$.

To find : Describe the transformation(s) ?

Solution :

Parent function $f(x) = \log(x)$

1) Translate the graph of function to horizontally compress

i.e. f(x)→f(ax), a>0

So,  $f(x) = \log(3x)$ i.e. horizontally compress with 3 units.

2) Translate the graph of function to the left with a unit

i.e. f(x)→f(x+a)

So,  $f(x) = \log(3x+6)$ i.e. Horizontal shift left with 6 units.

3) Translate the graph of function to the down with b unit

i.e. f(x)→f(x)-b

So,  $f(x) = \log(3x+6)-2$ i.e. Vertical shift down with 2 units.

4) Translate the graph of function by reflection about the y-axis

i.e. f(x)→f(-x)

So,  $f(x) = \log(-3x-6)-2$ i.e. Reflection about the y-axis.