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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.

Respuesta :

isyllus

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: [tex]f(x)=\log x[/tex]

Transformation function: [tex]f(x)=\log(-2x-4)+2[/tex]

Take -2 common from transform function f(x)

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

Now we see the step-by-step translation

[tex]f(x)=\log x[/tex]

Shift 2 unit left ( x → x+2 )

[tex]f(x)=\log(x+2)[/tex]

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

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

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

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

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

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

Simplify the function:

[tex]f(x)=\log(-2x-4)+2[/tex]

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

Answer and explanation:

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

Solution :

Parent function: [tex]f(x) =\log(x)[/tex]

Transformation function:  [tex]g(x) = \log(-2x-4) +2[/tex]

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

[tex]g(x) =\log(-2(x+2))+2[/tex]

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

[tex]f(x)=\log(x+2)[/tex]

Step 2 - Flip the graph about y-axis i.e, f(x)→ -f(x)

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

Step 3 -  Stretch horizontally by factor 2 i.e, f(x)→f(bx) stretch horizontally by b unit

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

Step 4 - Shift vertically up by 2 units i.e, f(x)→f(x)+b shifting vertically by b unit

[tex]f(x) =\log(-2(x+2))+2=g(x)[/tex]

In four steps the transformation is done.

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