What is the domain of the function y=3 in x graphed below?
2 answers:
Answer:
domain is x>0
Step-by-step explanation:
domain is the set of x values for which the function is defined
ln(negative value ) is undefined
So we take positive values for x because we have ln(x)
From the graph we can see that the given equation has a graph for x values greater than 0
the graph goes close to 0 but does not crosses y axis
So domain is x>0
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Answer:
The bounded area is 5 + 5/6 square units. (or 35/6 square units)
Step-by-step explanation:
Suppose we want to find the area bounded by two functions f(x) and g(x) in a given interval (x1, x2)
Such that f(x) > g(x) in the given interval.
This area then can be calculated as the integral between x1 and x2 for f(x) - g(x).
We want to find the area bounded by:
f(x) = y = x^2 + 1
g(x) = y = x
x = -1
x = 2
To find this area, we need to f(x) - g(x) between x = -1 and x = 2
This is:
We know that:
Then our integral is:
The right side is equal to:
The bounded area is 5 + 5/6 square units.
We performed the following operations:
If you multiply the parent function by a constant, you get a vertical stretch if the constant is greater than 1, a vertical compression if the constant is between 0 and 1. In this case the constant is 2, so we have a vertical stretch.
If you change the sign of a function, you reflect its graph across the x axis.
If you add a constant to a function, you translate its graph vertically. If the constant is positive, you translate upwards, otherwise you translate downwards. In this case, the constant is -1, so you translate 1 unit down.