Use function notation to write $g$ in terms of $f ( x ) = \sqrt { x }$.
$g ( x ) = - \frac { 1 } { 3 } \sqrt { x - 8 } + 7$

A) $g ( x ) = - f ( x - 8 ) + 6$

B) $\quad g ( x ) = - \frac { 1 } { 3 } f ( x ) - 1$

C) $\quad g ( x ) = - \frac { 1 } { 3 } f ( x - 8 ) + 7$

D) $g ( x ) = f ( x ) + 7$

E) $\quad g ( x ) = f ( x - 8 ) - \frac { 7 } { 3 }$

Question

Use function notation to write $g$ in terms of $f ( x ) = \sqrt { x }$.
$g ( x ) = - \frac { 1 } { 3 } \sqrt { x - 8 } + 7$

A) $g ( x ) = - f ( x - 8 ) + 6$

B) $\quad g ( x ) = - \frac { 1 } { 3 } f ( x ) - 1$

C) $\quad g ( x ) = - \frac { 1 } { 3 } f ( x - 8 ) + 7$

D) $g ( x ) = f ( x ) + 7$

E) $\quad g ( x ) = f ( x - 8 ) - \frac { 7 } { 3 }$

Quizplus · Accepted Answer

We can see that the function $g$ is formed by taking the square root function, shifting it right by 8 units, scaling it vertically by a factor of $-\frac{1}{3}$, and then shifting it up by 7 units. Using function notation, we can write this as: $$g(x) = -\frac{1}{3}f(x-8)+7$$ Since $f(x) = \sqrt{x}$, we can substitute this in to get: $$g(x) = -\frac{1}{3}\sqrt{x-8}+7$$ Therefore, the correct choice is $\boxed{\textbf{(C)}}$.

Use Function Notation to Write ggg In Terms Of f(x)=xf ( x ) = \sqrt { x }f(x)=x​

Use Function Notation to Write $g$ In Terms Of $f ( x ) = \sqrt { x }$