Question

(PLEASE HELP!) Determine the values for the pronumerals that make the following piece-wise functions continuous.​

Answer 1

• a = - 1
• b = 7

Given

• A piece-wise function, consisting of three lines.

In order to make the function continuous, the first and second pairs of lines should have common points.

Let's find the common points.

1. Intersection of the first two lines:

• - x = 2 + x
• -2x = 2
• x = - 1

This determines the value of a:

• a = - 1

2. Intersection of the second two lines:

• 2 + x = 2x - 5
• 2x - x = 2 + 5
• x = 7

This determines the value of b:

• b = 7

See the graph attached