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A feature that is common to all exponential functions of the form F of x equals bx is that they have a common horizontal asymptote at the negative axis?
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∙ 11y ago
x axis
Wiki User
∙ 11y ago
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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
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.
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 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).
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
Asymptote of x² times e to the power of x?
As x tends to negative infinity, the expression is asymptotically 0.
What is the exponential form of x to the negative 1?
-x1
The base of an exponential function cannot be a negative number?
True
If a function is negative at a test number it will reach zero before it reaches an asymptote?
Not necessarily. f(x) = -1-x2 is negative for any test value of x, it is asymptotically negative infinity, but it is NEVER zero.
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.
