Question

function 1 (graph) \\ function 2 \

$$\begin{tabular}{|c|c|} \\hline x & y \\\\ \\hline -2 & 2 \\\\ \\hline -1 & 0 \\\\ \\hline 0 & -2 \\\\ \\hline 1 & -4 \\\\ \\hline 2 & -6 \\\\ \\hline \\end{tabular}$$

\\ function 3 \\( y = 3x + 5 \\) \\ function 4 \\( \text{the slope is } -4 \text{ and the } y\text{-intercept is } 1 \\). \\ answer the following questions. \\ (a) which function has the graph with a \\( y \\)-intercept closest to 0? \\ \\( \circ \\) function 1 \\( \circ \\) function 2 \\( \circ \\) function 3 \\( \circ \\) function 4 \\ (b) which function has the graph with the greatest slope? \\ \\( \circ \\) function 1 \\( \circ \\) function 2 \\( \circ \\) function 3 \\( \circ \\) function 4 \\ (c) which functions have graphs with \\( y \\)-intercepts greater than 4? (circle all that apply) \\ function 1 \\ function 2 \\ function 3 \\ function 4

Explanation:

Step1: Find y-intercepts of all functions

• Function 1: From graph, y-intercept is $-1$
• Function 2: From table, when $x=0$, $y=-2$
• Function 3: From $y=3x+5$, y-intercept is $5$
• Function 4: Given y-intercept is $1$

Step2: Compare distances to 0

• $|-1|=1$, $|-2|=2$, $|5|=5$, $|1|=1$
• Closest to 0: Function 1 (distance 1)

Step3: Find slopes of all functions

• Function 1: Use points $(1,3)$ and $(0,-1)$: $\frac{3-(-1)}{1-0}=4$
• Function 2: Use $(0,-2)$ and $(1,-4)$: $\frac{-4-(-2)}{1-0}=-2$
• Function 3: From $y=3x+5$, slope is $3$
• Function 4: Given slope is $-4$
• Greatest slope: $4$ (Function 1)

Step4: Check y-intercepts >4

• Function 1: $-1 < 4$; Function 2: $-2 < 4$; Function 3: $5 > 4$; Function 4: $1 < 4$
• Only Function 3 qualifies

Answer:

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