Question

function 1 (graph), function 2 (table with x: -2, -1, 0, 1, 2 and y: 8, 6, 4, 2, 0), function 3 (equation y = 5x - 5), function 4 (slope 1, y - intercept 1). answer the following questions. (a) which function’s graph is the least steep? options: function 1, function 2, function 3, function 4. (b) which function has the graph with the greatest y - intercept? options: function 1, function 2, function 3, function 4. (c) which functions have graphs with missing term less than - 3? (check all that apply.) options: function 1, function 2, function 3, function 4.

Explanation:

Step1: Find slopes of all functions

• Function 1: Use points $(0,-2)$ and $(1,-4)$

Slope $m_1=\frac{-4-(-2)}{1-0}=-2$

• Function 2: Use $x=-2,y=8$ and $x=-1,y=6$

Slope $m_2=\frac{6-8}{-1-(-2)}=-2$

• Function 3: $y=5x-5$, so $m_3=5$
• Function 4: Given $m_4=1$

Take absolute values for steepness: $|m_1|=2$, $|m_2|=2$, $|m_3|=5$, $|m_4|=1$

Step2: Find y-intercepts of all functions

• Function 1: Graph crosses y-axis at $(0,-2)$, so $b_1=-2$
• Function 2: Use $x=0,y=4$, so $b_2=4$
• Function 3: $y=5x-5$, so $b_3=-5$
• Function 4: Given $b_4=1$

Step3: Compare slopes to -3

Check each slope:

• $m_1=-2 > -3$
• $m_2=-2 > -3$
• $m_3=5 > -3$
• $m_4=1 > -3$

Answer:

(a) Function 4
(b) Function 2
(c) None of the functions