In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achi

Question

Vsevolod

2 months ago

5

In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achi

eve the graph of g(x) = log(-2x-4) + 2.

Mathematics

2 answers:

tester [12.3K] · Answer 1 · 2026-03-17T00:04:10+03:00

Response:

Move 2 units to the left

Reflect the graph across the y-axis

Expand horizontally by a factor of 2

Lift vertically by 2 units

Detailed explanation:

Provided:

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

Transformed function: $f(x)=\log(-2x-4)+2$

Extract -2 from the transformation function f(x)

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

Now, we can observe the step-by-step transformations

$f(x)=\log x$

Move 2 units to the left ( x → x+2 )

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

Reflect the graph across the y-axis ( (x+2) → - (x+2) )

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

Expand horizontally by a factor of 2 [ -x(x+2) → -2(x+2) ]

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

Lift vertically by 2 units [ f(x) → f(x) + 2 ]

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

Simplifying the function:

$f(x)=\log(-2x-4)+2$

Thus, applying four transformation steps results in the new function $f(x)=\log(-2x-4)+2$

tester [12.3K] · Answer 2 · 2026-03-17T00:04:26+03:00

In order to determine the transformations applied to the parent function, $f(x) =\log(x)$ , to derive the graph of $g(x) = \log(-2x-4) +2$ , the following steps outline the process: First, we will express the transformed function by factoring out -2. Step 1 involves shifting the graph 2 units to the left, which is represented mathematically as f(x)→f(x+b) for a b unit left shift in the parent function. Step 2 consists of reflecting the graph over the y-axis, so f(x) transforms to -f(x). Step 3 entails horizontally stretching the graph by a factor of 2, where f(x) morphs into f(bx) for a horizontal stretch of b units. Finally, Step 4 requires shifting the graph upwards by 2 units, or f(x) becoming f(x)+b for a vertical shift of b units. After completing these four steps, the transformation is accomplished.