The graph represents the piecewise function

Mathematics

2 answers:

tester [92]2 years ago

6 0

<h2>Answer:</h2>

Hence, we have:

f(x)= 2x-1 when x ≤ -1

x+4 when x ≥ 1

<h2>Step-by-step explanation:</h2>

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:

$f(x)-(-3)=\dfrac{-5-(-3)}{-2-(-1)}\times (x-(-1))\\\\\\f(x)+3=\dfrac{-5+3}{-2+1}\times (x+1)\\\\\\f(x)+3=2(x+1)\\\\\\f(x)=2x+2-3\\\\\\f(x)=2x-1$

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:

$f(x)-5=\dfrac{6-5}{2-1}\times (x-1)\\\\\\f(x)-5=x-1\\\\\\f(x)=x-1+5\\\\\\f(x)=x+4$

svlad2 [7]2 years ago

3 0

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

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drek231 [11]

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