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(-2x-4) + 1.

Answer 1

The parent function  that is f(x) = log(x)  is transformed  firstly, to log(x+2)

since, we can see after that we can directly convert it to log(2x+4)

and after one reflection it will become log(-2x-4)

NOTE: Reflection is the mirror image so it will directly comes to the opposite quadrant

after one reflection graph will  be shifted to  one unit up vertically.

Answer 2

Answer:

1) Shift 2 unit left

2) Flip the graph about y-axis

3) Stretch horizontally by factor 2

4) Shift vertically up by 1 units

Step-by-step explanation:

Given:

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

Transformation function: $g(x) = \log(-2x-4) + 1$

Re-write the transformed function by taking -2 common,

$g(x) = \log(-2(x+2)) + 1$

Step 1 -

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

Shift 2 unit left i.e, f(x)→f(x+b) shifting left by b unit

$f(x)=\log(x+2)$

Step 2 -

Flip the graph about y-axis i.e, f(x)→ -f(x)

$f(x)=\log[-(x+2)]$

Step 3 -

Stretch horizontally by factor 2 i.e, f(x)→f(bx) stretch horizontally by b unit

$f(x)=\log[-2(x+2)]$

Step 4 -

Shift vertically up by 1 units i.e, f(x)→f(x)+b shifting vertically by b unit

$f(x)=\log[-2(x+2)]+1$

Thus, In 4 steps transformation is done.