1. **State the problem:** We are given four functions and need to compare their y-intercepts and slopes. 2. **Given information:** - Function 3: $y = -3x - 4$ (slope $m = -3$, y-intercept $b = -4$) - Function 4: slope $m = 4$, y-intercept $b = 2$ - Function 1: y-intercept approximately $-1$ (from graph), slope steep increasing (positive, exact value unknown) - Function 2: points $(-1,6), (0,5), (1,4), (2,3)$; y-intercept is $5$ (value at $x=0$) 3. **(a) Which functions have y-intercepts greater than 3?** - Function 1: y-intercept $oxed{-1}$ (not greater than 3) - Function 2: y-intercept $5$ (greater than 3) - Function 3: y-intercept $-4$ (not greater than 3) - Function 4: y-intercept $2$ (not greater than 3) **Answer:** Function 2 only. 4. **(b) Which function has the greatest slope?** - Function 1: steep increasing, slope positive but unknown exact value - Function 2: slope calculated from points: slope $= \frac{4-5}{1-0} = \frac{-1}{1} = -1$ - Function 3: slope $-3$ - Function 4: slope $4$ Comparing slopes: $4 >$ unknown positive slope of Function 1? Since Function 1 is steep increasing but no exact value, assume less than 4. **Answer:** Function 4 has the greatest slope. 5. **(c) Which function has y-intercept closest to 0?** - Function 1: $-1$ (distance to 0 is 1) - Function 2: $5$ (distance 5) - Function 3: $-4$ (distance 4) - Function 4: $2$ (distance 2) Closest to 0 is Function 1 with y-intercept $-1$. **Final answers:** (a) Function 2 (b) Function 4 (c) Function 1