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.
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 4
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=(5x)^3[/tex]
Comparing the parent function with the given function, we can see that the x-value of the parent function has been multiplied by 5.
Therefore, the transformation is:
[tex]y=f(5x) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{5}[/tex]
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
Question 5
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=(x+5)^3+5[/tex]
Comparing the parent function with the given function, we can see that there are a series of transformations:
Step 1
5 has been added to the x-value of the parent function.
[tex]f(x+5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units left}[/tex]
Step 2
5 has then been added to function.
[tex]f(x+5)+5 \implies f(x+5) \: \textsf{translated}\:5\:\textsf{units up}[/tex]
Transformation: Left 5, Up 5
Question 6
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=(x-5)^3-5[/tex]
Comparing the parent function with the given function, we can see that there are a series of transformations:
Step 1
5 has been subtracted from the x-value of the parent function.
[tex]f(x-5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units right}[/tex]
Step 2
5 has then been subtracted from function.
[tex]f(x-5)-5 \implies f(x-5) \: \textsf{translated}\:5\:\textsf{units down}[/tex]
Transformation: Right 5, Down 5
Learn more about graph transformations here:
https://brainly.com/question/27845947
