Which best describes the asymptote of an exponential function of the form F(x) = bx?A.Vertical asymptote at x = 1B.Horizontal asymptote at y = 0C.Vertical asymptote at x = 0D.Horizontal asymptote at y = 1SUBMITarrow_backPREVIOUS
Question
Which best describes the asymptote of an exponential function of the form F(x) = bx?A.Vertical asymptote at x = 1B.Horizontal asymptote at y = 0C.Vertical asymptote at x = 0D.Horizontal asymptote at y = 1SUBMITarrow_backPREVIOUS
Solution
The best description for the asymptote of an exponential function of the form F(x) = bx is B. Horizontal asymptote at y = 0.
Here's why:
An exponential function of the form F(x) = bx, where b > 0 and b ≠ 1, has a horizontal asymptote at y = 0. This is because as x approaches negative infinity, the value of F(x) gets closer and closer to 0 but never actually reaches 0. This is the definition of a horizontal asymptote.
On the other hand, vertical asymptotes occur when the function approaches infinity or negative infinity as x approaches a certain value. In the case of the exponential function F(x) = bx, there is no value of x that will make the function approach infinity or negative infinity, so there are no vertical asymptotes.
Therefore, the correct answer is B. Horizontal asymptote at y = 0.
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Which term below correctly completes the following sentence?If a function has a vertical asymptote at a certain x-value, then the function is _____ at that value.A.zeroB.undefinedC.rationalD.negativeSUBMITarrow_backPREVIOUS
An exponential function is written as F(x) = a • bx, where the coefficient a is a constant, the base b is positive but not equal to 1, and the exponent x is ______.A.an integerB.any numberC.positiveD.negativeSUBMITarrow_backPREVIOUS
Vertical asymptotes at x = 4) Horizontal asymptote at y
The function 𝑓(𝑥)=𝑎𝑏𝑥+𝑐f(x)= bx+ca has a vertical asymptote at:
Find the y-intercept and the horizontal asymptote of the following exponential function: 𝑓(𝑥)=1(3)𝑥+6 Group of answer choicesy-intercept: (0,9); horizontal asymptote: y=3y-intercept: (0,7); horizontal asymptote: y=6y-intercept: (0,4); horizontal asymptote: y=6y-intercept: (0,4); horizontal asymptote: y=1y-intercept: (0,6); horizontal asymptote: y=7
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