Question

which rules define the function graphed below? y y = x, y = 5 y = x + 2, y = 5 y = x, x = 5 y = x + 2, x = 5 (3,5) 6 5 4 3 2 (0, 2) 1 -3 -2 -1 1 2 3 4 5 6 7 x -1 -2 -3 -4

Explanation:

Step1: Find the equation of the first - line segment

The line segment passes through the points $(0,2)$ and $(3,5)$. The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The y - intercept $b = 2$ (since the line crosses the y - axis at $y = 2$). The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{5 - 2}{3-0}=1$. So the equation of the line is $y=x + 2$ for $0\leq x\leq3$.

Step2: Find the equation of the second - line segment

For $x\geq3$, the value of $y$ is constant at $y = 5$.

Answer:

$y=x + 2,y = 5$ (the second option)