Question

In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB.
Graph of two intersecting lines. The line f of x is solid and goes through the points 0, 4, and 4, 0 and is shaded below the line. The other line g of x is solid, and goes through the points 0, negative 1 and 2, 5 and is shaded below the line.

The graph represents which system of inequalities?

y ≤ −3x − 1
y ≤ −x − 4

y > −3x + 1
y ≤ −x − 4

y < 3x − 1
y ≤ −x + 4

y ≤ 3x − 1
y ≥ −x + 4

Answer 1

Answer:

• y < 3x − 1
• y ≤ −x + 4

Step-by-step explanation:

As per the given graph we have:

Function f with dotted line (> or < sign), increasing function (slope is positive), y-intercept of -1 and shaded area A is to the right (so < sign), so this represents the inequality:

• f(x) < 3x - 1

Function g with solid line (≥ or ≤ sign), decreasing function (slope is negative), y-intercept is 4 and shaded area B is to the left (so ≤ sign), so this represents the inequality:

• g(x) ≤ -x + 4

Correct system is C:

• y < 3x − 1
• y ≤ −x + 4