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Q: For all values of a and b that make Fx equals a bx a valid exponential function the graph always has a horizontal asymptote at y equals 0?

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Exponential growth goes infinitely up. Exponential decay goes infinitely over always getting closer to the x axis but never reaching it. ADDED: An exponential decay trace's flat-looking region has its own special name: an "asymptote".

It is often a good idea. But consider this: it may not have a value on the wrong side of the asymptote. Try graphing y = 1/x.

No, it will always have one.

The horizontal axis is reserved for the independent variable in a function. Time is always an independent variable in time-based functions. However, duration can be dependent. It depends on what's being plotted.

The point you desire, is (1, 0).The explanation follows:b0 = 1, for all b; thus,logb(1) = 0, for all b.On the other hand, logb(0) = -∞,which explains the vertical asymptote at the y-axis.

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The exponential function is always increasing or decreasing, so its derivative has a constant sign. However the function is solution of an equation of the kind y' = ay for some constant a. Therefore the function itself never changes sign and is MORE?

Exponential growth goes infinitely up. Exponential decay goes infinitely over always getting closer to the x axis but never reaching it. ADDED: An exponential decay trace's flat-looking region has its own special name: an "asymptote".

It is often a good idea. But consider this: it may not have a value on the wrong side of the asymptote. Try graphing y = 1/x.

No, it will always have one.

No. An exponential function is not linear. A very easy way to understand what is and what is not a linear function is in the word, "linear function." A linear function, when graphed, must form a straight line.P.S. The basic formula for any linear function is y=mx+b. No matter what number you put in for the m and b variables, you will always make a linear function.

neither linear nor exponential functions have stationary points, meaning their gradients are either always +ve or -ve

The horizontal axis is reserved for the independent variable in a function. Time is always an independent variable in time-based functions. However, duration can be dependent. It depends on what's being plotted.

The point you desire, is (1, 0).The explanation follows:b0 = 1, for all b; thus,logb(1) = 0, for all b.On the other hand, logb(0) = -∞,which explains the vertical asymptote at the y-axis.

Horizontal lines always have a slope of 0.

The y-intercept for a pure exponential relationship is always 1.

Yes.

No. It is not uncommon for the layers to be shifted out of a horizontal position.