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Answer:
[tex]f(x)=\left\{\begin{array}{ccc}3x+10&\text{for}&x\le -2\\2x-7&\text{for}&x>4\end{array}\right.[/tex]
Step-by-step explanation:
We observe that the left line segment has a rise of 3 for each run of 1. Its slope is ...
m = rise/run = 3/1 = 3
It goes through point (-2, 4), so its equation can be written ...
y = m(x -h) +k . . . . line with slope m through (h, k)
y = 3(x +2) +4 . . . . fill in known values
y = 3x +10 . . . . . . . simplify — equation of left line
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The right segment has a rise of 2 for each run of 1. Its slope is ...
m = 2/1 = 2
Then the equation of the line through point (4, 1) is ...
y = 2(x -4) +1
y = 2x -7
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Taking into account solid and open circles, the equation for the function is ...
[tex]f(x)=\left\{\begin{array}{ccc}3x+10&\text{for}&x\le -2\\2x-7&\text{for}&x>4\end{array}\right.[/tex]
