Answer:
f(-2) = 2
f(0) = 3
f (4) = -1
Step-by-step explanation:
The equation of the straight line passing through the points (0,3) and (-4,1) is
[tex]\frac{y - 1}{1 - 3} = \frac{x - (- 4)}{-4 - 0}[/tex]
⇒ 2(y - 1) = x + 4
⇒ 2y - 2 = x + 4
⇒ 2y = x + 6
⇒ [tex]y = \frac{1}{2} x + 3[/tex]
Again, the equation of the line passing through the points (0,1) and (4,-1) is
[tex]\frac{y - (- 1)}{- 1 - 1} = \frac{x - 4}{4 - 0}[/tex]
⇒ - 2 ( y + 1) = x - 4
⇒ - 2y = x - 2
⇒ [tex]y = 1 - \frac{1}{2}x[/tex]
Therefore, the function is defined as
[tex]f(x) = \frac{1}{2} x + 3[/tex] for x ≤ 0 ........... (1) and
[tex]f(x) = 1 - \frac{1}{2}x[/tex] for x > 0 ............ (2)
Therefore, f(-2) = 2 from equation (1).
f(0) = 3 from equation (1)
And f (4) = -1 from equation (2). (Answer)
Answer:
f(-2) = 2
f(0) = 3
f(4) = -1
Step-by-step explanation:
The equation of the line passing through (0,3) and (-4,1) will be
y-y_{1} = m\times (x-x_{1} )
m = \frac{3-1}{0+4}
therefore
y - 3 = \frac{1}{2}\times x
therefore f(-2) = (\frac{1}{2}\times -2) + 3 = 2
since we have a closed circle at (0,3)
the function value at (0,3) will be 3
therefore f(0) = 3
The equatiom of the line passing through (0, 1) and (4,-1) will be
y-y_{1} = m\times (x-x_{1} )
m = \frac{1+1}{0-4}
therefore
y - 1 = \frac{-x}{2}
therefore f(4) = \frac{-4}{2} + 1 = -1 .
