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krok68 [10]
1 year ago
12

NO LINKS!!! What is the transformation f(x)= x^3:

Mathematics
2 answers:
Mama L [17]1 year ago
6 0

Answer:

4.  Horizontal shrink by a factor of ¹/₅

5.  Left 5, Up 5

6.  Right 5, Down 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.

<u>Transformations</u>

For a > 0

f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}

f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}

f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}

f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}

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

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

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

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

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

<u>Question 4</u>

\textsf{Parent function}: \quad f(x)=x^3

\textsf{Given function}: \quad f(x)=(5x)^3

Comparing the parent function with the given function, we can see that the <u>x-value of the parent function</u> has been <u>multiplied</u> by 5.

Therefore, the transformation is:

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

As a > 1, the transformation visually is a compression in the x-direction, so we can also say:  Horizontal shrink by a factor of ¹/₅

<u>Question 5</u>

\textsf{Parent function}: \quad f(x)=x^3

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

Comparing the parent function with the given function, we can see that there are a series of transformations:

<u>Step 1</u>

5 has been <u>added to the x-value</u> of the parent function.

f(x+5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units left}

<u>Step 2</u>

5 has then been <u>added to function</u>.

f(x+5)+5 \implies f(x+5) \: \textsf{translated}\:5\:\textsf{units up}

<u>Transformation</u>:  Left 5, Up 5

<u>Question 6</u>

\textsf{Parent function}: \quad f(x)=x^3

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

Comparing the parent function with the given function, we can see that there are a series of transformations:

<u>Step 1</u>

5 has been <u>subtracted from the x-value</u> of the parent function.

f(x-5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units right}

<u>Step 2</u>

5 has then been <u>subtracted from function</u>.

f(x-5)-5 \implies f(x-5) \: \textsf{translated}\:5\:\textsf{units down}

<u>Transformation</u>:  Right 5, Down 5

Learn more about graph transformations here:

brainly.com/question/27845947

sasho [114]1 year ago
6 0

Answer:

4) Horizontal shrink by a factor of 1/5

5) Left 5, Up 5

6) Right 5, Down 5

Explanation:

Main parent function: f(x) = x^3

4.) f(x) = (5x)^3

Comparing it with f(ax) which gives horizontal compression when a > 1 or horizontal stretch when 0 < |a| < 1 by a factor of 1/a

The function has been compressed horizontally by a factor of 1/5.

5.) f(x) = (x+5)^3 + 5

Comparing with f(x + c) + d, gives function moved c units left, d units up.

The function has moved 5 units left and 5 units up.

6.) f(x) = (x-5)^3 - 5

Comparing with f(x - c) - d, gives function moved c units right, d units down.

The function has moved 5 units right, 5 units down.

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