Describe any clusters of data from the scatter plot
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Hello!
A cubic function is in the form of .
All cubic functions have a domain of all real numbers, the range also has a range of all real numbers.
Interval notation is used for representing a function/interval as a pair of numbers. Parentheses and brackets are used to show if the endpoints of a given function/interval are included or excluded. Brackets allow the endpoints to be included while parentheses exclude the endpoint.
Our first instinct would be that the domain is written as [-∞, ∞], but that is incorrect. Infinity is not a number, but it is a concept. This means that they are excluded from the domain.
Therefore, the domain of the function f(x) is (-∞, ∞).
Notice the picture below
no matter what value "y" may have, "x" will always be 1
no matter what value "y" may have, "x" will always be 1
Given function is
now we need to find the value of k such that function f(x) continuous everywhere.
We know that any function f(x) is continuous at point x=a if left hand limit and right hand limits at the point x=a are equal.
So we just need to find both left and right hand limits then set equal to each other to find the value of k
To find the left hand limit (LHD) we plug x=-4 into 3x+k
so LHD= 3(-4)+k
To find the Right hand limit (RHD) we plug x=-4 into
so RHD=
Now set both equal
k=-0.47
<u>Hence final answer is -0.47.</u>