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