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Which graph shows the transformation of the function f(x) = e^x where the function is translated three units to the right, vertically compressed by a factor of 1/4, and then translated six units down.

Which graph shows the transformation of the function fx ex where the function is translated three units to the right vertically compressed by a factor of 14 and class=
Which graph shows the transformation of the function fx ex where the function is translated three units to the right vertically compressed by a factor of 14 and class=
Which graph shows the transformation of the function fx ex where the function is translated three units to the right vertically compressed by a factor of 14 and class=
Which graph shows the transformation of the function fx ex where the function is translated three units to the right vertically compressed by a factor of 14 and class=
Which graph shows the transformation of the function fx ex where the function is translated three units to the right vertically compressed by a factor of 14 and class=

Respuesta :

Original function is f(x) = [tex]e^x[/tex]

For this y intercept = 1. i.e. passes through (0,1)

First it is translated three units to the right.

So y = [tex]e^(x-3)[/tex]

When vertically compressed by a factor of 1/4 we have

y = [tex]4e^(x-3)[/tex]

Next is translated 6 units down

i.e. new graph would be

y = [tex]4e^(x-3)[/tex]+6

When x =3, y =6.

When y =-6, x tends to infinity.

i.e. y =-6 is an asymptote

Hence we find that 4th graph is the correct answer.


isyllus

Answer:

C is correct graph.

Step-by-step explanation:

Given: [tex]f(x)=e^x[/tex]

Now we do some operation on function f(x)

Step 1: f(x) is translated 3 units to the right.

For a unit right translation, x changes to

[tex]x\rightarrow x-a[/tex]

Therefore, [tex]f(x)=e^{x-3}[/tex]

Step 2: Vertical compressed by a factor of [tex]\frac{1}{4}[/tex]

For vertical compressed. f(x) changes to a f(x)  

[tex]f(x)=\frac{1}{4}e^{x-3}[/tex]

Step 3: Translated 6 unit down

For this translation, y changes to

[tex]y\rightarrow y-6[/tex]

Therefore, [tex]f(x)=\frac{1}{4}e^{x-3}-6[/tex]

Final function after three steps we get,

[tex]f(x)=\frac{1}{4}e^{x-3}-6[/tex]

Please see the attachment for correct graph.

Thus, C is correct graph.

Ver imagen isyllus

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