Respuesta :

semsee45

Answer:

1.  Vertical shrink by a factor of ¹/₅

2.  Right 5

3.  Up 5

Step-by-step explanation:

Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.

Transformations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]

Identify the transformations that take the parent function to the given function.

Question 1

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=\dfrac{1}{5}x^3[/tex]

Comparing the parent function with the given function, we can see that the parent function has been multiplied by ¹/₅.

Therefore, the transformation is:

[tex]y=\dfrac{1}{5}\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:\dfrac{1}{5}[/tex]

As 0 < a < 1, the transformation visually is a compression in the y-direction, so we can also say:  Vertical shrink by a factor of ¹/₅

Question 2

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=(x-5)^3[/tex]

Comparing the parent function with the given function, we can see that 5 has been subtracted from the x-value of the parent function.

Therefore, the transformation is:

[tex]f(x-5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units right}[/tex]

Question 3

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=x^3+5[/tex]

Comparing the parent function with the given function, we can see that  5 has been added to the parent function.

Therefore, the transformation is:

[tex]f(x)+5 \implies f(x) \: \textsf{translated}\:5\:\textsf{units up}[/tex]

Learn more about graph transformations here:

https://brainly.com/question/27845947

fieryanswererft

Answer:

1) Vertical shrink by a factor of 1/5

2) Right 5

3) Up 5

Explanation:

Given main function: f(x) = x³

1.) f(x) = 1/5 (x³)

Comparing with a(f(x)) which gives vertical stretch or compression.

Here the function f(x) has been shrinked vertically by a factor of 1/5

2.) f(x) = (x - 5)³

Comparing with f(x - c) which gives horizontal translation c units right.

Here the function f(x) has been shifted 5 units to the right.

3.) f(x)= x³ + 5​

Comparing it with f(x) + d which gives vertical translation d units up.

Here the function f(x) has been moved 5 units up.

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