Question

The graph represents the piecewise function

Answer 1

ok, so so we gots from x≤-1 and x≥1 for the bounds

hmm, the x≤-1 one

hmm, looks like the y intercept is -1 and the slope is 2/1
y=2x-1
test (-1,-3)
works
test (-2,-5)
works

yep

2x-1 is first blank



the other one

seems to have y intercept at 4 and slope of 1
y=1x+4
y=x+4
this works because I tested it



top left: 2x-1
top right: x≤-1 or x is less than or equal to -1
bottom left: x=4
bottom left: x≥1 or x is greater than or equal to 1

Answer 2

The piecewise function is

`f(x)=\begin{cases}2x-1&\text{ if }x\leq-1\\ x+4&\text{ if } x\geq1 \end{cases}`

Explanation:

From the given graph it is noticed that the graph is divides into two pieces.

The first function is defined for all values of x which are less than or equal to -1. The second function is defined for all values of x which are greater than or equal to 1.

The equation of line which passing through two points is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The first line is passing trough (-1,-3) and (-2,-5).

`y-(-3)=(-5-(-3))/(-2-(-1))(x-(-1))`

`y+3=(-2)/(-1)(x+1)`

`y+3=2(x+1)`

`y=2x+2-3`

`y=2x-1`

For
`x\leq-1` the function is defined as,

`f(x)=2x-1`

Similarly the second line is passing through (1,5) and (2,6).

`y-5=(6-5)/(2-1)(x-1)`

`y-5=1(x-1)`

`y=x+4`

For
`x\geq-1` the function is defined as,

`f(x)=x+4`

Therefore, the piecewise function is,

`f(x)=\begin{cases}2x-1&\text{ if }x\leq-1\\ x+4&\text{ if } x\geq1 \end{cases}`