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2 answers:
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To determine the graph that corresponds to the given inequality, first, let's write the inequality for y:
Add 3 to both sides of the expression
Divide both sides by 5
The inequality is for the values of y greater than or equal to 2/5x+3/5, which means that in the graph the shaded area will be above the line determined by the equation.
Determine two points of the line to graph it:
-The y-intercept is (0,3/5)
- Use x=5 to determine a second point
The second point is (5,13/5)
Plot both points to graph the line. Then shade the area above the line.
The graph that corresponds to the given inequality is the second one.
Answer:
Options (1), (2), (3), (6)
Step-by-step explanation:
Given functions are,
f(x) =
h(x) =
Option (1)
y-intercept of function 'h',
x = 0,
h(x) =
= 5
So y-intercept is (0, 5)
True.
Option (2)
Domain of function 'h' is (-∞, ∞)
True
Option (3)
As x approaches ∞, h(x) approaches ∞.
True.
Option (4)
For x intercept,
h(x) = 0
2x = (-5)³
2x = -125
x = -62.5
So the x-intercept is (-62.5, 0)
False.
Option (5)
Range of the function 'h' is (-∞, ∞)
False
Option (6)
As x approaches to -∞, h(x) approaches to -∞.
Since, range of the function is (-∞, ∞), given statement is true.
Therefore, Options (1), (2), (3), (6) are correct.