Question

The graph represents the piecewise function

Answer 1

left equatoin seems to be x is less than or equal to -1
the slope seems to be 2 and y intercep tis -1 so 2x-1


right equation is x is greater than or equal to 1
slope is 1 and y intercept is 4 so x+4




top left blank is x+4, top right blank is x is greater than or equal to 1
bottom left blank is 2x-1, bottom right blank is x is less than or equal to -1

Answer 2

Hence, we have:

f(x)= 2x-1 when x ≤ -1

x+4 when x ≥ 1

Explanation:

• After looking at the graph we observe that in the region: x ≤ -1

The graph is a straight line that passes through (-1,-3) and (-2,-5)

Hence, the equation of line is:

`f(x)-(-3)=(-5-(-3))/(-2-(-1))* (x-(-1))\\\\\\f(x)+3=(-5+3)/(-2+1)* (x+1)\\\\\\f(x)+3=2(x+1)\\\\\\f(x)=2x+2-3\\\\\\f(x)=2x-1`

• Also, in the interval x ≥ 1

The graph is a straight line that passes through (1,5) and (2,6)

Hence, the equation of line is:

`f(x)-5=(6-5)/(2-1)* (x-1)\\\\\\f(x)-5=x-1\\\\\\f(x)=x-1+5\\\\\\f(x)=x+4`