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What is the meaning of asymptote?
An asymptote is the tendency of a function to approach infinity as one of its variable takes certain values. For example, the function y = ex has a horizontal asymptote at y = 0 because when x takes extremely big, negative values, y approaches a fixed value : 0. Asymptotes are related to limits.
What is the formula for a rational function with x intercepts at x equals 3 and x equals negative 2. y intercept at y equals 12. a hole at x equals 1 and no horizontal asymptote?
f(x) = 2*(x-3)*(x+2)/(x-1) for x ≠1
Can the base of an exponential function be a negative number?
Yes, but remember that 2 negatives is a positive. so -2 to the 2nd power would be 4, but -2 to the 3rd power would be -8.
What does a graph of exponential growth look like?
graph y = k^x where k is >1. it will have a y-intercept of (0,1) because anything to the zero power = 1. It then increases rapidly in the 1st quadrant. The graph also passes thru (1,k) in te first quad. In the second quadrant, as the x value becomes more negative, the graph approaches the x -axis, this is called an asymptote, because the y values become smaller and smaller. All x values are negative in the 2nd quad thus creating reciprocals (defn of neg exponent). The graph passes thru (-1, 1/k) in 2nd quad. EX y = 2^x passes thru (0,1) y-intercept 1st quad thru (1,2) because k =2 and then increases rapidly 2nd quad thru (-1, 1/2) remember to approach the x-axis to the left,
What is the difference between zero slope and infinite slope?
Zero is when its a straight horizontal line It its going neither up or down Infinite is when its a straight vertical line You could say its positive or negative and it will forever going up or down You couldn't give it a slope number
Can a exponential functions be a negative number?
Exponential functions of the form ( f(x) = a \cdot b^x ), where ( a ) is a constant and ( b ) is a positive base, cannot yield negative values if ( a ) is positive. However, if ( a ) is negative, the function can take on negative values for certain inputs. In general, exponential functions are always positive when ( a ) is positive and ( b ) is greater than zero, but they can be negative if ( a ) is negative.
What is the horizontal asymptote of 5 divided by x minus 6?
-1
What is the meaning of asymptote?
An asymptote is the tendency of a function to approach infinity as one of its variable takes certain values. For example, the function y = ex has a horizontal asymptote at y = 0 because when x takes extremely big, negative values, y approaches a fixed value : 0. Asymptotes are related to limits.
In mathematics what is a symptote?
In mathematics, a asymptote is a straight line that a curve approaches but never quite reaches. Asymptotes can occur in various mathematical functions, such as rational functions or exponential functions. They are used to describe the behavior of a function as the input approaches infinity or negative infinity.
How do you find the horizontal asymptote of x3 times ex?
y=x3exyour first bet is to find the domain, the set of all possible x valuesfor x3 and e2in this case theres no restriictions in the domain meaning any real number can be used so you can consider everything properlynoww look at each segment x3 and ex as x approaches negative and positive infinityas as x approaches positive infinity x3 and ex both approach positive infinityno asymptote is seenBUT as x approaches negative infinity x3approaches negative infinity while ex approaches 0. now you have to see which one of the two moves fasterex approaches zero much faster than x3 approaches negative infinityso the horizontal asymptote is 0
What is a exponetial parent function?
An exponential parent function is a basic exponential function of the form ( f(x) = a \cdot b^x ), where ( a ) is a non-zero constant and ( b ) is a positive real number not equal to 1. The most common example is ( f(x) = 2^x ) or ( f(x) = e^x ). This function has a characteristic J-shaped curve, increasing rapidly for positive values of ( x ) and approaching zero as ( x ) becomes negative. It is defined for all real numbers and has a horizontal asymptote at ( y = 0 ).
What are characteristics of square root functions?
There are two square root functions from the non-negative real numbers to either the non-negative real numbers (Quadrant I) or to the non-positive real numbers (Quadrant IV). The two functions are symmetrical about the horizontal axis.
What is meaning of exponent with variable?
That you have an exponential function. These functions are typical for certain practical problems, such as population growth, or radioactive decay (with a negative exponent in this case).
Is a vertical asymptote undefined?
Yes, a vertical asymptote represents a value of the independent variable (usually (x)) where a function approaches infinity or negative infinity, and the function is indeed undefined at that point. This is because the function does not have a finite value as it approaches the asymptote. Thus, the vertical asymptote indicates a discontinuity in the function, where it cannot take on a specific value.
Do all exponential functions show growth over time?
If the exponent has the variable of time in it, then it will be either exponential growth (such as compound interest for example), or exponential decay (such as radioactive materials, or a capacitor discharging). If the time constant (coefficient of the time variable) is positive then it is growth, if the time constant is negative, then it is decay.
Can a exponential function be a negative number?
Well -x^3/4 would be exponential
What is the exponential form of x to the negative 1?
-x1
