mamaKelly2266
11.10.2019 •
Mathematics
How do the graphs of the functions f(x) = (3/2)^x and g(x) = (2/3)^2 compare?
Solved
Show answers
More tips
- H Health and Medicine How to Tan in a Tanning Bed? Tips and Recommendations...
- W Work and Career What is the Most In-Demand Profession in the Modern World?...
- A Auto and Moto How Can Parking Sensors Help Drivers?...
- H Health and Medicine What is the Normal Blood Sugar Level in a Healthy Person?...
- F Food and Cooking Red Caviar: How to Choose the Best?...
- C Computers and Internet Clearing Cache: How to Speed Up Your Browser...
- S Style and Beauty How are artificial nails removed?...
- S Style and Beauty Secrets of Tying a Pareo: 5 Ways...
- F Food and Cooking Everything You Need to Know About Pasta...
Answers on questions: Mathematics
- M Mathematics Jeremy has three pencils. one pencil is 9.36 inches long. the second pencil is 6.7 inches long. the third pencil is 8.025 inches long. will placing the pencils end to end make a total...
- M Mathematics The basics of managing money such as balancing a checkbook and making a budget are skills...
- M Mathematics Which best compares the slopes and y-intercepts of the linear functions f and g, where f=2x+2 and g is shown in the table?...
- M Mathematics Hurry simplify the expression (15^1/5)^5...
- M Mathematics What is the approximate scale factor dilating from the blue image to the red image? explain how you figured this out....
- M Mathematics Without doing the multiplication tell how many decimal places are in the product of 72.35 and 14.12...
- M Mathematics Consider the parent function f(x) = x². also, consider the function g(x) = -3(x-2)² +3. what is the vertex? (-2,3) (3,2) (2,3) (-2,-3)...
- M Mathematics The area of brians rectangular garden, in sqaure feet, can be foind by using expression 6(2x + 5y).use the distributive propeety to write an equivalent for the area of brians garden....
- M Mathematics You have 12000 invest and you want to keep your money invest for 8 years...
- M Mathematics Casey correctly wrote and solved a system of linear equations by substitution. in his work, he submitted an expression for one variable and solved for the other. this resulted in the...
Ответ:
First of all, you have a small typo in your question. The actual question is: How do the graphs of the functions f(x) = (3/2)^x and g(x) = (2/3)^x compare?
g(x) = (2/3)^2 is not even a function :)
Notice that the base of g(x) is the base of f(x) inverted. Every time you see that pattern expect a reflection about the y-axis.
Let's check it out why.
There are two types of reflections in exponential function
- Reflection about the x-axis
To reflect an exponential function about the x-axis, multiply the output of the function by -1. For example, to reflect the function f(x)=e^x about the x-axis, we multiply the output, e^2, of function by -1 to get f(x)=-e^x.
- Reflection about the y-axis.
To reflect the exponential function about the y-axis, multiply the input of the function by -1. For example, to reflect the function f(x)=e^x, we multiply the input, x, of the function by -1 to get f(x)=e^-x.
Let's multiply the output our of function f(x) and see what happens:
Remember that according to the laws of exponents to get rid of the minus sign in the exponent we just need to flip the fraction:
Look! We just transformed f(x) into g(x)! Proving that they are reflections of each other over the y-axis.
We can conclude that the correct answer is the graphs are reflections of each other over the y-axis.
Ответ:
The graphs are reflections of each other over the y-axis.
The g(x) function represents exponential decay.
The f(x) function represents exponential growth.
They have the same initial value.
Here, You can see in f(x) = (3/2)^x, where exponential is variable, which can be anything either positive or negative.
In function g(x) = (2/3)^2, denominator is greater than numerator, so their square will be smaller than the number itself. Hence, 2 is in power, it will show exponential decay.
In short, Your Answer would be Option B
Hope this helps!
Ответ:
Ignore the question it is wrong
Step-by-step explanation: