Find a formula for the function graphed. - A) $f ( x ) = \left\{ \begin{array} { l l } 4 , & x 0 \end{array} \right.$ C) $f ( x ) = \left\{ \begin{array} { l l } 4 , & x

Question

Find a formula for the function graphed.
- 
A) $f ( x ) = \left\{ \begin{array} { l l } 4 , & x < 0 \ x , & x \geq 0 \end{array} \right.$ 
B) $f ( x ) = \left\{ \begin{array} { l l } 4 , & x \leq 0 \ - x , & x > 0 \end{array} \right.$ 
C) $f ( x ) = \left\{ \begin{array} { l l } 4 , & x < 0 \ - x , & x \geq 0 \end{array} \right.$ 
D) $f ( x ) = \left\{ \begin{array} { l l } 4 , & x < 0 \ - 4 x , & x \geq 0 \end{array} \right.$

Quizplus · Accepted Answer

The function is a piecewise function with a "corner" or "break" at x = 0. At x < 0, the function is a horizontal line at y = 4, which can be written as f(x) = 4. At x ≥ 0, the function is a decreasing linear function with a y-intercept of 0 and a slope of -1, which can be written as f(x) = -x. Thus, the formula for the function is:

f(x) = {4, x < 0
       {-x, x ≥ 0

which matches choice C.

Find a Formula for the Function Graphed f(x)={4,x<0x,x≥0f ( x ) = \left\{ \begin{array} { l l } 4 , & x < 0 \\ x , & x \geq 0 \end{array} \right.f(x)={4,x,​x<0x≥0​

Find a Formula for the Function Graphed $f ( x ) = \left\{ \begin{array} { l l } 4 , & x < 0 \\ x , & x \geq 0 \end{array} \right.$