Question

Which rule defines the function in the graph? Two line segments on a coordinate plane that do not meet. The first segment begins at negative 3 comma negative 4, inclusive, and ends at 1 comma zero, non inclusive. The second segment begins at 2 comma 3, inclusive, and ends at 4 comma negative 3, inclusive. Group of answer choices f(x)={ x−1, if −3 ≤ x < 1 f(x)={ −3x+9, if 2 ≤ x ≤ 4 f(x)= { x−1 , if −3 < x ≤ 1 f(x)= {−3x+9 , if 2 < x < 4 f(x)={ x−1, if −3 ≤ x < 1 f(x)={ x−3, if 2 ≤ x≤ 4 f(x)={x−1, if −3 < x ≤ 1 f(x)={x−3, if 2 < x < 4

Answer 1

The correct option is;

f(x) = {x - 1 if -3 ≤ x < 1 f(x) = {-3·x + 9, if 2 ≤ x ≤ 4

Explanation:

The given coordinates of the points are;

For the first segment

Beginning point [-3, -4] (inclusive)

Endpoint (1, 0), (noninclusive)

For the second segment

Beginning point [2, 3] (inclusive)

Endpoint [4, -3] (inclusive)

The equation of the first segment is therefore;

y - 0 = (0 + 4)/(1 + 3)×(x - 1) = 1 × (x - 1)

y = x - 1

The equation of the second segment is found as follows;

y + 3 = (-3 - 3)/(4 - 2)×(x - 4) = -3 × (x - 4)

y + 3 = -3 × (x - 4) = -3·x + 12

y = -3·x + 12 - 3 = -3·x + 9

Therefore, we have;

f(x) = {x - 1 if -3 ≤ x < 1 and f(x) = {-3·x + 9, if 2 ≤ x ≤ 4