Answer:
3. Since the range of the original function is limited to y> 6, the domain of the inverse function is x ≥ 6.
Step-by-step explanation:
The domain of a function is the range of its inverse, and vice versa. The only answer choice that expresses this relationship is choice 3.
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Comment on the answer choice:
The slope of the function is undefined at x=4, so restricting the function domain to the portion with positive slope means the domain restriction of the function is x > 4. That also means the range restriction of the function is y > 6. The domain restriction of the inverse function is the same: x > 6, not x ≥ 6. The answer choice has an error.
Answer:
The equation for rational function for given asymptotes is
f(x)=(-4x^2-6)/{(x-3)(x+3)}
Step-by-step explanation:
Given:
vertical Asymptotes at x=3 and x=-3 and a horizontal asymptote at
y=-4 i.e parallel to x axis.
To find:
equation of a rational function i.e function in form p/q
Solution;
the equation should be in form of p/q
Numerator :denominator.
Consider f(x)=g(x)/h(x)
as vertical asymptote are x=-3 and x=3
denominator becomes, (x-3) and (x+3)
for horizontal asymptote to exist there should have same degrees in numerator and denominator which of '2'
when g(x) will be degree '2' with -4 as coefficient and dont have any real.
zero.
By horizontal asymptote will be (-4x^2 -6)
The rational function is given by
f(x)=g(x)/h(x)
={(-4x^2-6)/(x-3)(x+3)}.
<h2>
Answer:</h2>
A. It is a many-to-one function.
<h2>
Step-by-step explanation:</h2>
Hello! It will be a pleasure to help to figure out what's the correct answer to this problem. First of all, we have the following function:

When plotting this function, we get the red graph of the function shown below. So let's solve this as follows:
<h3>A. It is a many-to-one function.</h3>
True
A function is said to be many-to-one there are values of the dependent variable (y-values) that corresponds to more than one value of the independent variable (x-values). To test this, we need to use the Horizontal Line Test. So let's take the horizontal line
, and you can see from the first figure below that
is mapped onto
. so this is a many-to-one function.
<h3>B. It is a one-to-one function.</h3><h3>False</h3>
Since this is a many-to-one function, it can't be a one-to-one function.
<h3>C. It is not a function.</h3>
False
Indeed, this is a function
<h3>D. It fails the vertical line test.</h3>
False
It passes the vertical line test because any vertical line can intersect the graph of the function at most once. An example of this is shown in the second figure below.