Question

A line is in the x y coordinate plane. The line is labeled g(x). The line enters the viewing window in the second quadrant, goes down and to the right. As it travels, the line passes through the following points.

• (−5, 10)
• (−3, 4)
• (−5/3, 0)
• (−1, −2)
• (−2/3, −3)
• (0, −5)
• (2/3, −7)
• (1, −8)
• (5/3, −10)

The line exits the window in the fourth quadrant.

(a) Estimate

g(1).

g(1) =

(b) Estimate

g(−3).

g(−3) =

(c) Estimate x such that g(x) = 1.
x =

(d) Give the domain and range for g(x).
Domain:

[−10, 10](−∞, 0)    (−10, 6)(−∞, ∞)(−5, 5)

Range:

(−∞, ∞)(−5, 5)     [−10, 10](−∞, 0)(−10, 6)

(e) Estimate the vertical and horizontal intercepts for g(x). (If an answer does not exist, enter DNE.)

vertical intercept		(x, y) =
horizontal intercept		(x, y) =

Answer 1

1911)=-g g1-3) y=g(+3) -3+5 ta somain and range of g (a) Solh Ginan Points of line are (-5,10), (-3,4),(-3,0), 1-1,-2), (~2%, -3), 10,-5),(3; -7), (1,-8), 15/31010). gu) = -8 i.t " at aal • at x =-3 , 4 -:(+3) = 4 to find a g(x) = 1 then we have Equation of dine is given by (4-40) = 42-4, (x^2,) Hq - lat, (4, 4, )= (-5, 10) Q (M 25 Yz) = (~3,4) ie ly~10) = 4-10 (x+5) (4-10 ) = (x+5) (y-10) -3(x+5) y = -3% -15 +10 y=-3x - 5 y = g() = 1 I ~325) 4 =-3X -4 3 @ je g(x) = -3x-5 4. Domain is 1-00,00) {xlxe R} Range is (-00,00) y ly E.IR vertical intercept is (",y) = 10,-5) {Y- and intercept} Horizontal intercept b (y) = 45,0) 1x-axia Pretencept . 3 . = ہ