Question

the graph of f(x) is shown below. what are the values of a, b, c, and d in the definition of f(x) below? (graph and definition of f(x) shown in attached image)​

Answer 1

Explanation:

For the given piecewise function,

Let the equation of the segment AB is,

y = ax + 7 where x < -2

Since a point (-2, 3) lies on the given line,

3 = a(-2) + 7

3 - 7 = -2a

a = 2

Therefore, f(x) = 2x + 7 when x < -2

For the segment BC,

f(x) = 3 where -2 ≤ x ≤ 2

For the segment CD,

f(x) = bx + 9

Since a point (2, 3) lies on this segment,

f(2) = 2b + 9 = 3

2b = 3 - 9

b = -3

Therefore, equation of segment CD will be,

f(x) = (-3)x + 9 where x > 2