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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.

2 Answers

5 votes

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.

User Sorig
by
7.7k points
5 votes

Answer:

Shift 2 unit left

Flip the graph about y-axis

Stretch horizontally by factor 2

Shift vertically up by 2 units

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

User Jakub Turcovsky
by
8.1k points

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