Question

Find the first 3 interations here: g(x)=-1|x-2|+3 if you have an initial value of 0.5

Answer 1

Sample Answer:When a linear function is expressed in different forms, its slope and y-intercept remain the same. The slope from the equation is -1, and the y-intercept from the equation is 3. The slope from the table is -1, and the y-intercept from the table is −3. These are not the same functions.

Explanation:

Answer 2

• The first iteration = 1.5

• The 2nd iteration = 2.5

• The third iteration = 2.5

Explanation:

Considering the function

• 
  `g\left(x\right)=-1\:|\:x\:-\:2\:|\:+\:3`

• As the initial value = 0.5

• In order to determine the next iterate, apply the function g(x) to the previous one.

DETERMINING FIRST ITERATION:

`g\left(0.5\right)=-1\:|\:0.5\:-\:2\:|\:+\:3`

= -1 | 0.5 - 2 | + 3

= -1 | -1.5 | + 3

`\mathrm{Apply\:absolute\:rule}:\quad \left|-a\right|=a` ; | -1.5 | = 1.5

`=-1.5+3`

= 1.5

Thus, the first iteration = 1.5

DETERMINING SECOND ITERATION:

Putting the value of first iteration i.e. 1.5 into the original function to determine the 2nd iteration.

`g\left(1.5\right)=-1\:|\:1.5\:-\:2\:|\:+\:3`

as
`1.5 - 2 = -0.5`

`\mathrm{Apply\:absolute\:rule}:\quad \left|-a\right|=a` ; | -0.5 | = 0.5

`=-0.5+3`

= 2.5

Thus, the 2nd iteration = 2.5

DETERMINING THIRD ITERATION:

Putting the value of second iteration i.e. 2.5 into the original function to determine the 2nd iteration.

`g\left(2.5\right)=-1\:|\:2.5\:-\:2\:|\:+\:3`

`\mathrm{Apply\:absolute\:rule}:\quad \left|a\right|=a,\:a\ge 0`

`=-0.5+3` as
`2.5-2=0.5`

= 2.5

Thus, the third iteration = 2.5