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) + 2.

Answer 1

Answer:

Shift 2 unit left

Flip the graph about y-axis

Stretch horizontally by factor 2

Shift vertically up by 2 units

Step-by-step explanation:

Given:

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

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

Take -2 common from transform function f(x)

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

Now we see the step-by-step translation

$f(x)=\log x$

Shift 2 unit left ( x → x+2 )

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

Flip the graph about y-axis ( (x+2)  → - (x+2) )

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

Stretch horizontally by factor 2 [ -x(x+2) → -2(x+2) ]

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

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

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

Simplify the function:

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

Hence, Using four step of transformation to get new function $f(x)=\log(-2x-4)+2$

Answer 2

Answer and explanation:

To find : Describe the transformation(s) that take place on the parent function, $f(x) =\log(x)$, to achieve the graph of $g(x) = \log(-2x-4) +2$

Solution :

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

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

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

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

Step 1 -  Shift 2 unit left i.e, f(x)→f(x+b) shifting left by b unit  in parent function,

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

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

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

In four steps the transformation is done.