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Is every integer a rational number or is every rational number an integer?
Every integer is a rational number.
How will you determine if a graph is a function or a mere relation?
You use the "vertical line test". If anywhere you can draw a vertical line that goes through two points of the graph, the relation is not a function; otherwise, it is a function. This is just another way of saying that in a function for every x value (input) there is AT MOST one y value (output).
Is every number a rational number?
No but every integer is a rational number and numbers that can be expressed as fractions are also rational numbers
Why is any parabola that opens upward or downward a function?
It is a function because for every point on the horizontal axis, the parabola identified one and only one point in the vertical direction.
What is the horizantal line test and vertical line test?
Horizonatal line test is a test use to determine if a function is one-to-one. If a horizontal line intersects a function's graph more than once, then the function is not one-to-one. A one-to-one function is a function where every element of the range correspons to exactly one element of the domain. Vertical line test is a test used to determine if a function is a function or relation. If you can put a vertical line through graph and it only hits the graph once, then it is a function. If it hits more than once, then it is a relation.
Does every rational function have an asymptote?
No if the denominators cancel each other out there is no asymptote
Does every rational function have more than one vertical asymp tote?
No.The equation x/(x^2 + 1) does not have a vertical asymptote.
Does every rational function has at least one horizontal asymptote?
Nope not all the rational functions have a horizontal asymptote
Is it true that the function has a vertical asymptote at every x value where its numerator is zero and you can make a table for each vertical asymptote to find out what happens to the function there?
Every function has a vertical asymptote at every values that don't belong to the domain of the function. After you find those values you have to study the value of the limit in that point and if the result is infinite, then you have an vertical asymptote in that value
Does every undefined value of fx lead to a vertical asymptote?
No. For example, in real numbers, the square root of negative numbers are not defined.
A function will always be a vertical line?
A function can never be a vertical line, because it then fails the definition of a function: every x value outputs only 1 y value. The vertical line test will determine if a relation is a function. If a vertical line intersects the graph of the function at more than one place, it is not a function.
Is the cardinality of an infinitely countable set the same as the rational numbers?
Yes. There is an injective function from rational numbers to positive rational numbers*. Every positive rational number can be written in lowest terms as a/b, so there is an injective function from positive rationals to pairs of positive integers. The function f(a,b) = a^2 + 2ab + b^2 + a + 3b maps maps every pair of positive integers (a,b) to a unique integer. So there is an injective function from rationals to integers. Since every integer is rational, the identity function is an injective function from integers to rationals. Then By the Cantor-Schroder-Bernstein theorem, there is a bijective function from rationals to integers, so the rationals are countably infinite. *This is left as an exercise for the reader.
How can you tell if a graph is a function?
The vertical line test can be used to determine if a graph is a function. If two points in a graph are connected with the help of a vertical line, it is not a function. If it cannot be connected, it is a function.
Is there an instance when a linear equation is not a function?
Yes, a vertical line is linear, but it is not a function, because every point on the line has the same x value.
Is every integer a rational number or is every rational number an integer?
Every integer is a rational number.
How is y 3x a function?
y=3x is a function because if you graph it, it passes the Vertical Line Test (draw a vertical line anywhere, a function will not touch the line twice or more). Also, it only has one y value for every x value.
Why is y equals 3x a function?
y=3x is a function because if you graph it, it passes the Vertical Line Test (draw a vertical line anywhere, a function will not touch the line twice or more). Also, it only has one y value for every x value.
