How does the graph of y = 3x compare to the graph of y = 3–x?
2 answers:
<h2>Answer and explanation:</h2>
In this problem, we have two functions. Let's call the first functions as:
and the second function:
So we can compare this functions as follows:
- f(x) has a positive slope while g(x) has a negative slope.
- f(x) passes through the origin of the system of coordinates while g(x) cuts the y-intercept at
- g(x) has an x-intercept at
while f(x) cuts the origin.
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The true statement for f(x)=b^x is the function is always decreasing function.
We have given,
f(x)=b^x where 0<b<1
<h3>What is the domain?</h3>Domain is all possible values of x for which any function is defined
We can select any values of x for which function
It will be defined for all real x
So, the domain is
The range is all possible values of y for which x is defined
we are given that b is positive
The value of the function will always be positive
So, the range is
y>0
The x-intercept:
Set f(x)=0 and then we can solve for x
f(x)=b^x=0
x is undefined
The x-intercept does not exist
Increasing or decreasing:
Since, 0<b<1
The b is a positive value less than 1
As we increase the value of, will keep decreasing
This is decreasing function
To learn more about the function visit: