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What else can I help you with?
Why is graph paper used when sketching?
to know exactly what point your going to draw on
Can the graph of a rational function have both a horizontal and oblique asymptote?
Piece wise functions can do everything. Take two pieces of two rational functions, one have a horizontal asymptote as x goes to -infinity and the other have a slanted (oblique) one as x goes to +infinity. It is still a rational function.
What does a rational function look like?
A rational function is a function defined as the ratio of two polynomial functions, typically expressed in the form ( f(x) = \frac{P(x)}{Q(x)} ), where ( P(x) ) and ( Q(x) ) are polynomials. The graph of a rational function can exhibit a variety of behaviors, including vertical and horizontal asymptotes, and can have holes where the function is undefined. The degree of the polynomials affects the function's end behavior and the locations of its asymptotes. Overall, rational functions can represent complex relationships and are often used in calculus and algebra.
Is fx a function if fx equals 0 if x is a rational number and 1 if x is an irrational number?
Yes. It is a piece-wise function with the limit: lim{x->0}= 0 You graph both parts as two series of dotted lines since there are infinite rational and irrational possibilities
How do you determine if the graph of a function is concave down without looking at the graph?
If you can differentiate the function, then you can tell that the graph is concave down if the second derivative is negative over the range examined. As an example: for f(x) = -x2, f'(x) = -2x and f"(x) = -2 < 0, so the function will be everywhere concave down.
When you are given a graph how can you come up with a rational function equation?
You cannot, necessarily. Given a graph of the tan function, you could not.
Why doesnt the graph of a rational function cross its vertical asymptote?
It can.
Why do we set the denominator to zero to graph a rational function?
We set the denominator to zero to find the singularities: points where the graph is undefined.
Can the graph of a rational function have more than one vertical asymptote?
Assume the rational function is in its simplest form (if not, simplify it). If the denominator is a quadratic or of a higher power then it can have more than one roots and each one of these roots will result in a vertical asymptote. So, the graph of a rational function will have as many vertical asymptotes as there are distinct roots in its denominator.
Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even?
If the point (x,y) is on the graph of the even function y = f(x) then so is (-x,y)
What is a rational function graph?
The Equation of a Rational Function has the Form,... f(x) = g(x)/h(x) where h(x) is not equal to zero. We will use a given Rational Function as an Example to graph showing the Vertical and Horizontal Asymptotes, and also the Hole in the Graph of that Function, if they exist. Let the Rational Function be,... f(x) = (x-2)/(x² - 5x + 6). f(x) = (x-2)/[(x-2)(x-3)]. Now if the Denominator (x-2)(x-3) = 0, then the Rational function will be Undefined, that is, the case of Division by Zero (0). So, in the Rational Function f(x) = (x-2)/[(x-2)(x-3)], we see that at x=2 or x=3, the Denominator is equal to Zero (0). But at x=3, we notice that the Numerator is equal to ( 1 ), that is, f(3) = 1/0, hence a Vertical Asymptote at x = 3. But at x=2, we have f(2) = 0/0, 'meaningless'. There is a Hole in the Graph at x = 2.
How you can use the zeros of the numerator and the zeros of the denominator of a rational function to determine whether the graph lies below or above the x-axis in a specific interval?
Discuss how you can use the zeros of the numerator and the zeros of the denominator of a rational function to determine whether the graph lies below or above the x-axis in a specified interval?
Why is graph paper used when sketching?
to know exactly what point your going to draw on
Can the graph of a rational function have both a horizontal and oblique asymptote?
Piece wise functions can do everything. Take two pieces of two rational functions, one have a horizontal asymptote as x goes to -infinity and the other have a slanted (oblique) one as x goes to +infinity. It is still a rational function.
What does an undefined graph look like?
An undefined graph typically occurs when there is a division by zero in a mathematical equation, resulting in an infinite or undefined value. In a graph, this would manifest as a vertical line or asymptote where the function approaches infinity or negative infinity. This can happen, for example, when plotting the graph of a rational function where the denominator equals zero at a certain point.
What does a rational function look like?
A rational function is a function defined as the ratio of two polynomial functions, typically expressed in the form ( f(x) = \frac{P(x)}{Q(x)} ), where ( P(x) ) and ( Q(x) ) are polynomials. The graph of a rational function can exhibit a variety of behaviors, including vertical and horizontal asymptotes, and can have holes where the function is undefined. The degree of the polynomials affects the function's end behavior and the locations of its asymptotes. Overall, rational functions can represent complex relationships and are often used in calculus and algebra.
Place the steps to sketch the graph of a rational function in the appropriate order?
answer is:Find the function's zeros and vertical asymptotes, and plot them on a number line.Choose test numbers to the left and right of each of these places, and find the value of the function at each test number.Use test numbers to find where the function is positive and where it is negative.Sketch the function's graph, plotting additional points as guides as needed.
