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contestada

Given the following function equations, state all of the transformations present on the graph of f(x)

4f(x-1)
-f(2x)
f(-x)+2

Respuesta :

Answer:

See explanation

Step-by-step explanation:

f(x) ==> 4f(x-1)

1. f(x) ==> f(x-1)      Translate the graph 1 unit to the right

2. f(x-1) ==> 4f(x-1) Vertical stretch by a factor of 4

f(x) ==> -f(2x)

1. f(x) ==> f(2x)     Horizontal compression by a factor of 1/2

2. f(2x) ==> -f(2x)    Reflection over the x-axis

f(x) ==> f(-x)+2

1. f(x) ==> f(-x)     Reflection over the y-axis

2. f(-x) ==> f(-x)+2    Translate the graph 2 units up.

semsee45

Answer:

1)  Translated 1 unit right and stretched vertically by a factor of 4.

2)  Compressed horizontally by a factor of ¹/₂ and reflected in the x-axis.

3)  Reflected in the y-axis and translated 2 units up.

Step-by-step explanation:

Transformations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ 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]\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of $a$} \\& \textsf{If }a > 1 \textsf{ it is stretched by a factor of $a$}\\& \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of $a$}\end{aligned}[/tex]

[tex]\begin{aligned} y=f(ax) \implies & f(x) \: \textsf{stretched/compressed horizontally by a factor of $\dfrac{1}{a}$} \\ & \textsf{If }a > 1 \textsf{ it is compressed by a factor of $\dfrac{1}{a}$}\\ & \textsf{If }0 < a < 1 \textsf{ it is stretched by a factor of $\dfrac{1}{a}$}\end{aligned}[/tex]

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

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

Transformation 1

Given:  

  • [tex]4f(x-1)[/tex]

Transformations

[tex]f(x-1) \implies f(x) \: \textsf{translated}\:1\:\textsf{unit right}[/tex]

[tex]4\:f(x) \implies f(x) \: \textsf{stretched vertically by a factor of}\: 4[/tex]

Transformation 2

Given:

[tex]-f(2x)[/tex]

Transformations

[tex]f(2x) \implies f(x) \: \textsf{ compressed horizontally by a factor of $\dfrac{1}{2}$}[/tex]

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

Transformation 3

Given:

[tex]f(-x)+2[/tex]

Transformations

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

[tex]f(x)+2 \implies f(x) \: \textsf{translated}\:2\:\textsf{units up}[/tex]

Learn more about transformations here:

https://brainly.com/question/28041916

https://brainly.com/question/27815602

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