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To have asymptote -4, put (x + 4) in the denominator. To have asymptote 2, put (x-2) in the denominator. For the hole at -5, put (x+5) in numerator and denominator. So we have:

(x + 5)/((x + 4)(x + 5)(x - 2)), now multiply this by a constant (A), then set x = 0, and solve for A such that y = 0.5.

A(0 + 5)/(4*5*(-2)) = -A/8. So if -A/8 = 1/2, then A = -4.

Q: Determine the equation of a rational function with a hole at x -5 a y-intercept of 0.5 and vertical asymtotes at x -4 and x 2?

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For the equation (9x^2)/(x^2+4)

To determine the trend of linear function graph or equation you would simply look at the slope of the line. This is represented by the m in the equation, f(x) = mx + b.

If x2 is negative it will have a maximum value If x2 is positive it will have a minimum value

The cosine function is mathematical equation to determine the adjacent angle of a triangle. The cosine of an angle is the ratio of the length of the hypotenuse: so called because it is the sine of the co-angle.

An equation just has an equal sign. A function is basically just an equation without one!

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For the equation (9x^2)/(x^2+4)

Set 0=(denominator of the System Transfer Function), this is the Characteristic Equation of that system. This equation is used to determine the stability of a system and to determine how a controller should be designed to stabilize a system.

If the function is a straight line equation that passes through the graph once, then that's a function, anything on a graph is a relation!

To determine the trend of linear function graph or equation you would simply look at the slope of the line. This is represented by the m in the equation, f(x) = mx + b.

If x2 is negative it will have a maximum value If x2 is positive it will have a minimum value

The cosine function is mathematical equation to determine the adjacent angle of a triangle. The cosine of an angle is the ratio of the length of the hypotenuse: so called because it is the sine of the co-angle.

You can tell if an equation is a function if for any x value that you put into the function, you get only one y value. The equation you asked about is the equation of a line. It is a function.

In general you cannot. Any set of ordered pairs can be a graph, a table, a diagram or relation. Any set of ordered pairs that is one-to-one or many-to-one can be an equation, function.

a function rule

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The graphical way is probably the simplest. Draw a graph of the equation. Hold a ruler parallel to the y axis and slide it from left to right. If, at any point, the ruler touches the graph at more than one point then you do not have a function.