How do the graphs of the functions f(x) = (3/2)^x and g(x) = (2/3)^2 compare?

Asked by maham237 @ 22/12/2020 in Mathematics viewed by 287 People

Answered by maham237 @ 22/12/2020

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:

$f(x)=(\frac{3}{2} )^x$

$f(-x)=(\frac{3}{2} )^{-x}$

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:

$f(x)=(\frac{2}{3} )^x$ 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.

How do the graphs of the functions f(x) = (3/2)^x and g(x) = (2/3)^2 compare?

Similar Questions

Which graph models the function f(x) = −2(3)x?

Which graph models the function f(x) = −4(2)x?

Which graph represents the function f(x) = log10(x) + 2?

How does the graph of g(x) = 3x – 2 compare to the graph of f(x) = 3x?

Which graph is the sequence defined by the function f(x) = 3(2)x-1?

Which graph represents the function f(x) = (x – 5)2 + 3?

The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1.

The graphs of functions f(x) and g(x) = f(x) + k are shown below: the value of k is ___.

The graph of f(x) = x2 is translated to form g(x) = (x – 2)2 – 3.

What transformations change the graph of f(x) to the graph of g(x) f(x)=-7x^2 g(x)=-35x^2+5

Let g(x) be the reflection of f(x) = x 2 + 3 in the x-axis. what is the function rule for g(x)?

Which graph represents the function f(x) = |x + 3|?

Which graph represents the function f(x) = |x| – 4?

The function f(x) is shown on the graph. what is f(0)?

Which best describes the graph of the function f(x) = 4(1.5)x?

Most viewed questions in Mathematics

Unit 6 similar triangles homework 2 similar figures answer key

All things algebra unit 7 polygons and quadrilaterals answer key

Gina wilson all things algebra 2016 answer key unit 11

Unit 1 geometry basics homework 4 angle addition postulate answers

Unit 6 exponents and exponential functions homework 8 answer key

The manager of a vacation resort believes that the ages

What is 271 403 rounded to the nearest ten thousand

Unit 1 geometry basics homework 3 angle relationships answer key

Homework 2 parallelograms

Why would a prism beat a sphere in a competition?

John wants to send a letter to peter

An artist sells a painting for 20.50 but uses 5.75

Unit 4 congruent triangles homework 1 classifying triangles answer key

Unit 4 congruent triangles homework 2 angles of triangles

Compare the values of the 2s and 5s in 55220