Answer:
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.
Step-by-step explanation:
Transformations
[tex]\textsf{For $a > 0$}[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]
[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]
[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]
[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}[/tex]
[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}[/tex]
Question 6
Parent function:
[tex]f(x)=\sqrt{x}[/tex]
Stretched horizontally by a factor of 1/2:
Multiply the x-variable by 2:
[tex]\implies f(2x)=\sqrt{2x}[/tex]
Stretched vertically by a factor of 4:
Multiply the function by 4:
[tex]\implies4f(2x)=4\sqrt{2x}[/tex]
Question 7
Parent function:
[tex]f(x)=\lfloor x \rfloor[/tex]
Stretched horizontally by a factor of 1/3:
Multiply the x-variable by 3:
[tex]\implies f(3x)=\lfloor 3x \rfloor[/tex]
Translated 4 units down:
Subtract 4 from the function:
[tex]\implies f(3x)-4=\lfloor 3x \rfloor-4[/tex]
