Question

Sam entered three functions into a graphing calculator, y1 = x + 2, y2 = x2 + 2, and y3 = 2x. A portion of the table created by those functions is shown below.
x 2,3,4
y1 4,5,6
y2 6,11,18
y3 4,8,16
Choose = , < , or > so that each statement is true.
When x = 0, y1__________ y2
When x = 5, y2__________ y3
Choose y1, y2, and y3 so that the statement is true.
When x = -1,____ <____ < _____.

Answer 1

For this case we have the following functions:
 $y1 = x + 2 y2 = x ^ 2 + 2 y3 = 2 ^ x$
 
 When x = 0 we have:
 For y1:
 $y1 = 0 + 2 y1 = 2$
 For y2:
 $y2 = 0 ^ 2 + 2 y2 = 0 + 2 y2 = 2$
 Therefore, we have to:
 $y1 = y2$

 When x = 5 we have:
 For y2:
 $y2 = 5 ^ 2 + 2 y2 = 25 + 2 y2 = 27$
 For y3:
 $y3 = 2 ^ 5 y3 = 32$
 Therefore, we have to:
 $y2 \ \textless \ y3$

 When x = -1 we have:
 For y1:
 $y1 = -1 + 2 y1 = 1$
 For y2:
 $y2 = (-1) ^ 2 + 2 y2 = 1 + 2 y2 = 3$
 For y3:
 $y3 = 2 ^ {-1} y3 = 1/2 y3 = 0.5$
 Therefore, we have to:
 $y3 \ \textless \ y1 \ \textless \ y2$

 Answer:
 When x = 0, y1 = y2
 When x = 5, y2 <y3
 When x = -1, y3 <y1 <y2