Question

function 1 (graph), function 2 (table: x -2, -1, 0, 1, 2; y 0, -1, -2, -3, -4), function 3: $y = 5x + 3$, function 4: slope -4, y - intercept 5. answer the following questions. (a) which functions have graphs with y - intercepts greater than 4? (check all that apply.) options: function 1, function 2, function 3, function 4. (b) which function has the graph with the greatest slope? options: function 1, function 2, function 3, function 4. (c) which function has the graph with a y - intercept closest to 0? options: function 1, function 2, function 3, function 4.

Explanation:

Step1: Find y-intercepts of all functions

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

Step2: Find slopes of all functions

• Function 1: Use two points from the graph, e.g., $(0, -4)$ and $(2, 2)$. Slope $m=\frac{2-(-4)}{2-0}=\frac{6}{2}=3$
• Function 2: Use two table points, e.g., $(0, -2)$ and $(1, -3)$. Slope $m=\frac{-3-(-2)}{1-0}=-1$
• Function 3: Using $y=mx+b$, $m=5$
• Function 4: Given slope = $-4$

Step3: Answer part (a)

Identify functions with y-intercept $>4$: Only Function 4 (y-intercept=5) meets this.

Step4: Answer part (b)

Compare slopes: $5 > 3 > -1 > -4$. The largest slope is 5, from Function 3.

Step5: Answer part (c)

Calculate absolute values of y-intercepts to find closeness to 0:

• $|-4|=4$, $|-2|=2$, $|3|=3$, $|5|=5$. The smallest is 2, from Function 2.

Answer:

(a) Function 4
(b) Function 3
(c) Function 2