Write a calculation and a result that represents a number that is 5 greater than 3.
2 answers:
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Answer:
a. Domain: (-∞, ∞)
Range: (0,∞)
b. Domain: (-∞, ∞)
Range: (0,∞)
c. Domain: (-∞, ∞)
Range: (-∞,0)
d. Domain: (-∞, ∞)
Range: (-∞,0)
e. Domain: (-∞, ∞)
Range: (0,∞)
Step-by-step explanation:
These equations are all exponential functions. Exponential functions are curves which approach a horizontal asymptote usually at y=0 or the x-axis unless a value has been added to it. If it has, the curve shifts. None of these have that and their y - values remain between 0 and ∞. This is the range, the set of y values.
However, the range of exponentials can change based on the leading coefficient. If it is negative the graph flips upside down and its range goes to -∞. C and D have this. Their range is (-∞, 0)
In exponential functions, the x values are usually not affected and all are included in the function. Their domain is (-∞, ∞). All of these equations have this domain.
a. Domain: (-∞, ∞)
Range: (0,∞)
b. Domain: (-∞, ∞)
Range: (0,∞)
c. Domain: (-∞, ∞)
Range: (-∞,0)
d. Domain: (-∞, ∞)
Range: (-∞,0)
e. Domain: (-∞, ∞)
Range: (0,∞)
Answer:
y = 4.
Step-by-step explanation:
I suppose that this question relates to the image that can be seen below.
In the image, the green line represents the exponential function and the blue line represents the linear function.
The y-value after which the exponential function will always be greater than the linear function is the y-value where bot graphs intersect, such that after that point, the blue line starts increasing fast, and is always above the green line.
In this case, this point is the second intersection, and we can see that this intersection happens in the point (2, 4)
Remember that the usual notation for points is (x, y).
Then the y-value after which the exponential function will always be greater than the linear function is y = 4.
