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Darya [45]
3 years ago
12

Describe the domain and range of y=2(3)^x-2+5

Mathematics
2 answers:
evablogger [386]3 years ago
8 0

Answer:

the domain is "the set of all real numbers."

the range of the given function is (5, infinity)

Step-by-step explanation:

This is an exponential function.  For the sake of clarity you must enclose "x - 2" inside parentheses:  f(x) = 2(3)^(x-2).  This function is defined for all real x-values, so the domain is "the set of all real numbers."  

Focusing on  (3)^x:  This has the same shape as the basic exponential y = e^x; the graph starts in Quadrant II and increases with x, more and more rapidly as you pass x = 0.  The functions y = e^x and that of y = 3^x are always positive.  Likewise in the case of f(x) = 2(3)^(x-2):  the function is always positive.  If we look at f(x) = 2(3)^(x-2) alone, we conclude that the domain is (0, infinity).  But that " + 5 " in y=2(3)^(x-2) + 5 translates the entire graph of f(x) = 2(3)^(x-2) upward by 5 units.

Thus, the range of the given function is (5, infinity).

allochka39001 [22]3 years ago
5 0

Answer:

Step-by-step explanation:

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1.
the slope of the line y=3x+2 is the coefficient of x, that is 3.

2.
the slope of any line perpendicular to the line y=3x+2, is m, such that:

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3. 
so any line with equation y=-1/3x+k is perpendicular to y=3x+2.

moreover, the line y=-1/3x (so k=0) is the line passing through the origin
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to find this point:

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x*10/3=-2

x= \frac{-2*3}{10} = \frac{-6}{10}=-0.6


thus y is :  (-1/3)(-6/10)=0.2



Answer: (-0.6, 0.2)

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