Question

NO LINKS! Please help me with these problems. Part 2
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Answer 1

For question 6 :

> Vertical stretch by 4 ( Multiply y co-ordinates by a)

> Horizontal compress by 2 ( Multiply x co-ordinates by 1/a)

For question 7 :

> Horizontal compress by 3 (Multiply x co-ordinates by 1/a)

> Graph moved down 4.

I hope this is what you looking for.

Answer 2

6. Stretched horizontally by a factor of 1/2 and stretched vertically by a factor of 4.

7. Stretched horizontally by a factor of 1/3 and translated 4 units down.

Explanation:

Transformations

`\textsf{For $a > 0$}`

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

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

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

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

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

`f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $(1)/(a)$}`

`-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}`

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

Question 6

Parent function:

`f(x)=√(x)`

Stretched horizontally by a factor of 1/2:

Multiply the x-variable by 2:

`\implies f(2x)=√(2x)`

Stretched vertically by a factor of 4:

Multiply the function by 4:

`\implies4f(2x)=4√(2x)`

Question 7

Parent function:

`f(x)=\lfloor x \rfloor`

Stretched horizontally by a factor of 1/3:

Multiply the x-variable by 3:

`\implies f(3x)=\lfloor 3x \rfloor`

Translated 4 units down:

Subtract 4 from the function:

`\implies f(3x)-4=\lfloor 3x \rfloor-4`