Which of the following inequalities matches the graph? x −1 x −1 y −1 y −1
2 answers:
Answer:
<h2>D.</h2>Step-by-step explanation:
The complete question is
Which of the following inequalities matches the graph?
<em>Graph of an inequality with a solid horizontal line through the point (0, -1) and shading above the line</em>
A. x less than or greater to -1
B. x greater than or equal to -1
C. y less than or greater to -1
D. y greater than or equal to -1
The given description of the graph specifies "a solid horizontal line", when such line is solid, that means the proper inequality sign includes equality. This means that the viable answers are B and D.
Then, the description states that the horizontal line goes through (0,-1), that means the equation of the line is . And if the shading area is above the line, that means all solutions are more than -1, which implies the symbol "greater than or equal to -1".
Therefore, the right answer is D.
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F(x) = -2x²
g(x) = 2x - 4
f(x) = g(x)
-2x² = 2x - 4
-2x² - 2x = 2x - 2x - 4
-2x² - 2x + 4 = -4 + 4
-2x² - 2x + 4 = 0
-2(x²) - 2(x) - 2(-2) = 0
-2(x² - x - 2) = 0
-2 -2
x² - x - 2 = 0
x² + 2x - x - 2 = 0
x(x) + x(2) - 1(x) - 1(2) = 0
x(x + 2) - 1(x + 2) = 0
(x - 1)(x + 2) = 0
x - 1 = 0 or x + 2 = 0
+ 1 + 1 - 2 - 2
x = 1 or x = -2
f(x) = g(x)
-2x² = 2x - 4
-2(-2)² = 2(-2) - 4
-2(4) = -4 - 4
-8 = -8
or
f(x) = g(x)
-2x² = 2x - 4
-2(1)² = 2(1) - 4
-2 = 2 - 4
-2 = -2
Solution Sets: {(-2, -8), (1, -2)}
g(x) = 2x - 4
f(x) = g(x)
-2x² = 2x - 4
-2x² - 2x = 2x - 2x - 4
-2x² - 2x + 4 = -4 + 4
-2x² - 2x + 4 = 0
-2(x²) - 2(x) - 2(-2) = 0
-2(x² - x - 2) = 0
-2 -2
x² - x - 2 = 0
x² + 2x - x - 2 = 0
x(x) + x(2) - 1(x) - 1(2) = 0
x(x + 2) - 1(x + 2) = 0
(x - 1)(x + 2) = 0
x - 1 = 0 or x + 2 = 0
+ 1 + 1 - 2 - 2
x = 1 or x = -2
f(x) = g(x)
-2x² = 2x - 4
-2(-2)² = 2(-2) - 4
-2(4) = -4 - 4
-8 = -8
or
f(x) = g(x)
-2x² = 2x - 4
-2(1)² = 2(1) - 4
-2 = 2 - 4
-2 = -2
Solution Sets: {(-2, -8), (1, -2)}