x axis
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.
f(x) = 2*(x-3)*(x+2)/(x-1) for x ≠1
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.
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,
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
-1
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.
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
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.
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).
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.
Well -x^3/4 would be exponential
As x tends to negative infinity, the expression is asymptotically 0.
-x1
True
Not necessarily. f(x) = -1-x2 is negative for any test value of x, it is asymptotically negative infinity, but it is NEVER zero.
No. For example, in real numbers, the square root of negative numbers are not defined.