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 labeled AB.

A

`y \leqslant - 2 + 3 \\ y \leqslant x + 3`
B

`y \geqslant - 2x + 3 \\ y \geqslant x + 3`
C

`y \leqslant - 3x + 2 \\ y \leqslant - x + 2`
D

`y > - 2x + 3 \\ y > x + 3`
​

Answer 1

b

Explanation:

Answer 2

`\large\boxed{A.\ y\leq-2x+3,\ y\leq x+3}`

Explanation:

<, > - dotted line

≤, ≥ - solid line

<, ≤ - shaded region below the line

>, ≥ - shaded region above the line

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The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept → (0, b)

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

From the graph we have the points:

(0, 3) - y-intercept → b = 3 (for both lines)

f(x)

(0, 3), (1, 1)

`m=(1-3)/(1-0)=(-2)/(1)=-2`

Substitute:

`f(x):\ y=-2x+3`

The shaded region is below the solid line. Therefore:
`y\leq-2x+3`

g(x):

(0, 3), (2, 5)

`m=(5-3)/(2-0)=(2)/(2)=1`

Substitute:

`g(x):\ y=1x+3=x+3`

The shaded region is below the solid line. Therefore:
`y\leq x+3`