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How are the graphs of exponential growth and exponential decay functions different?
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".
Is it true that you should always check a function's values on both sides of its 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.
Can a rational function have no vertical horizontal oblique asymptotes?
No, it will always have one.
Why time is always taken on horizontal axis?
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 graph of a logarithmic function in the form of F x equals logb x will always have a vertical asymptote at the y-axis and an x-intercept at the point?
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.
Why are the y-values of an exponential growth function either always greater than or less than the asymptote of the function?
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?
How are the graphs of exponential growth and exponential decay functions different?
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".
Is it true that you should always check a function's values on both sides of its 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.
Can a rational function have no vertical horizontal oblique asymptotes?
No, it will always have one.
Is an exponential function linear?
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.
Why time is always taken on horizontal axis?
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.
What slope do horizontal lines always have?
Horizontal lines always have a slope of 0.
The graph of a logarithmic function in the form of F x equals logb x will always have a vertical asymptote at the y-axis and an x-intercept at the point?
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.
What is a constant function?
A constant function is a function that always yields the same output value, regardless of the input. In other words, the function's output is a fixed value and does not depend on the input variable. Graphically, a constant function appears as a horizontal line.
Are exponential functions always concave up?
Yes.
How do you find the y-intercept of a exponential relationship from a table?
The y-intercept for a pure exponential relationship is always 1.
Is a horizontal slope always positive?
No, never.
