Question

function 1 (graph), function 2 (table: x -2,-1,0,1,2; y -7,-6,-5,-4,-3), function 3: $y = -5x - 3$, function 4: the slope is 4 and the y - intercept is 2. answer the following questions. (a) which function has the graph with the greatest y - intercept? $circ$ function 1 $circ$ function 2 $circ$ function 3 $circ$ function 4 (b) which functions have graphs with slopes less than - 4? (check all that apply.) $circ$ function 1 $circ$ function 2 $circ$ function 3 $circ$ function 4 (c) which functions graph is the least steep? function 1, function 2, function 3, function 4

Explanation:

Step1: Find y-intercepts for all functions

• Function 1: From graph, crosses y-axis at $(0,4)$, so y-intercept = 4
• Function 2: From table, when $x=0$, $y=-5$, so y-intercept = -5
• Function 3: $y=-5x-3$, y-intercept = -3
• Function 4: Given y-intercept = 2

Step2: Compare y-intercepts

Values: $4, -5, -3, 2$. Greatest is 4 (Function 1).

Step3: Find slopes for all functions

• Function 1: Use points $(0,4)$ and $(2,0)$. Slope $m=\frac{0-4}{2-0}=-2$
• Function 2: Use $(-2,-7)$ and $(-1,-6)$. Slope $m=\frac{-6-(-7)}{-1-(-2)}=1$
• Function 3: $y=-5x-3$, slope $m=-5$
• Function 4: Given slope $m=4$

Step4: Identify slopes < -4

Only $-5 < -4$ (Function 3).

Step5: Find absolute slopes (steepness)

• $|-2|=2$, $|1|=1$, $|-5|=5$, $|4|=4$. Smallest is 1 (Function 2).

Answer:

(a) Function 1
(b) Function 3
(c) Function 2