the graph of a function is shown. which function is represented by the graph? o $f(x)=\\begin{cases}x - 3, &…

the graph of a function is shown. which function is represented by the graph? o $f(x)=\\begin{cases}x - 3, & x < 0 \\\\ 3, & x \\geq 0\\end{cases}$ o $f(x)=\\begin{cases}x + 3, & x < 0 \\\\ 3, & x \\geq 0\\end{cases}$ o $f(x)=\\begin{cases}-x + 3, & x \\leq 0 \\\\ 3, & x > 0\\end{cases}$ o $f(x)=\\begin{cases}-x - 3, & x \\leq 0 \\\\ 3, & x > 0\\end{cases}$

the graph of a function is shown. which function is represented by the graph? o $f(x)=\\begin{cases}x - 3, & x < 0 \\\\ 3, & x \\geq 0\\end{cases}$ o $f(x)=\\begin{cases}x + 3, & x < 0 \\\\ 3, & x \\geq 0\\end{cases}$ o $f(x)=\\begin{cases}-x + 3, & x \\leq 0 \\\\ 3, & x > 0\\end{cases}$ o $f(x)=\\begin{cases}-x - 3, & x \\leq 0 \\\\ 3, & x > 0\\end{cases}$

Answer

Explanation:

Step1: Analyze left - hand side of graph

For (x\leq0), the line has a (y) - intercept of 3 and a slope of - 1. The slope - intercept form of a line is (y = mx + b), where (m) is the slope and (b) is the (y) - intercept. So the equation of the line for (x\leq0) is (y=-x + 3).

Step2: Analyze right - hand side of graph

For (x>0), the graph is a horizontal line at (y = 3), so the equation for (x>0) is (y = 3).

Answer:

(f(x)=\begin{cases}-x + 3, &x\leq0\3, &x>0\end{cases})