have answer dont understand?

Question

ok, in my algebra II book it says that y doesnt vary directly with x for the equation y=4/3x, but it does for y=4x/3

why?? i checked and they both travel throught the origin-- please explain your answers



alrite, the next question is this: how do you graph a function? ive found that x is less than or equal to three (this is domain). and that f(x) is less than or equal to -11 (this is range)-- so does this mean that i go to (-3,-11) and graph (with an open circle on the end of a line segment, instead of a line?)

what do open and closed circles indicate for a point on a graph? when do you use them?

Answer 1

Good Lord you people have trouble speaking plain english.
Varying directly just means that when X goes up, Y goes up. In the first case, when X goes up, Y will go down, so it flunks the test.

Answer 2

Direct Variation

When two variable quantities have a constant (unchanged) ratio, their relationship is called a direct variation.
It is said that one variable "varies directly" as the other.

The constant ratio is called the constant of variation.

The formula for direct variation is y = kx,
where k is the constant of variation.
"y varies directly as x"

Notice that y = 4/3x does not follow the rules set above. For something to have DIRECT VARIATION is must be equal or "on the same eye" as the other side of the equation.

Do you see that 3x lies in the DENOMINATOR and not the numerator on the right side of the equation? That is the reason why your first equation does not have direct variation.

Your second equation, y = 4x/3, is similar to the y = kx, where
k = 4 and x is the variable. K = the constant of the variation. In other words, k remains the same while the values of x and y change.

When dealing with direct variation, keep in mind that in order to have direct variation y and x or y and x MUST BE on the same "level" if you will. In math terms, it must be in the form
y = kx.

++++++++++++++++++++++

An open circle means that there is a HOLE in the graph at some function because there is division by zero for some given function, which DOES NOT exist. In other words, you cannot divide by zero. Division by zero will create a HOLE or open circle in the graph of any function.

Keep in mind that y = f(x) and that f(x) = y. They are interchangeable.

Example:

y = x + 3 is the same or can be written as f(x) = x + 3. Got it?

A closed circle means that there is NO HOLE in the graph at a particular function.

Here are the steps you need to know:

Graphing a Function
by Plotting Points

Step 1: Find at least four ordered pair solutions.

Functions can vary on what the graph looks like. So it is good to have a lot of points so that you can get the right shape of the graph, whether it be a straight line, curve, etc..

Step 2: Plot the points found in step 1.


Step 3: Draw the graph by connecting ALL the points.

Here are the basic shapes of some of the more common graphs of functions. Keep in mind that these are the basic shapes of these graphs. They can be shifted and stretched depending on the function given. A major goal is to recognize what type of function you are graphing and predict the basic shape from that before you even start.

Note that the domain and ranges that go with each one are also given.

SAMPLE:

Graph the function f(x) = x + 3.

Follow the steps above and try this one on your own. If you are still lost, write back.

Guido

Answer 3

The graph of y=4/(3x) does not travel through the origin. There is no point on the graph corresponding to x=0, because you would be dividing by zero when attempting to compute y.

As x increases, 4/(3x) decreases, so y varies inversely with x.

To graph a function, choose values of x that lie in the domain, and compute the corresponding y-values. Then, plot these points on your graph, and connect them with a curve. Be mindful of any points at which the function is undefined. For example, for y=4/(3x), you can use any x-values except x=0, but you would not connect the points (-1,-4/3) and (1,4/3), because this function has what you would call a "vertical asymptote" at x=0: y becomes infinite as x approaches 0.

Open and closed circles are used when the function has a discontinuity, or a break in its graph. The closed circle at (x,y) means that the point (x,y) is included in the graph, whereas the open circle means it is not. For example, if a function f(x) is defined by

f(x) = 0 for x < 0, and f(x) = 1 for x >= 0,

then the graph would consist of a horizontal line along y=0, coming from the left (that is, negative x) that would stop at x=0, and then, at that point, a horizontal line would begin at y=1 and continue to the right (for positive x). You would use a circle to indicate the end of the line along y=0 at the point (0,0), and at the beginning of the line along y=1 at the point (0,1), so that these points can easily be seen. However, you use an open circle at (0,0) and a closed circle at (0,1), because f(0)=1. That means (0,0) is not included in the graph of f(x), but (0,1) is.

Answer 4

"Directly" means any change in x is linearly reflected in y when multiplied by the slope, which is a scaling factor. That's the basic definition of a linear function, which is a line.

y= 4/(3x) is an "inverse" relationship, the graph of the function is not a line, its a curve.

Closed circles mean that the point at the center of the circle is part of the of the domain, e.g., "less than or equal." while open circles represent "less than" or "greater than" limits in the domain.

Answer 5

y varies inversely with x, meaning as x grows, y shrinks, and vice versa.

The graph would be all points where x <= 3 and where y <= -11, which is sort of an infinite square with it's "upper right" corner at (3,-11).

Open means all points greater than (or outside) the equation, and closed means all points less than (or inside) the equation.