Your question seems very confused. The normal convention of the Cartesian coordinate system would place negative numbers below the x axis, so that any curve approaching negative infinity would curve downward, not upward.
When the limit as the function approaches from the left, doesn't equal the limit as the function approaches from the right. For example, let's look at the function 1/x as x approaches 0. As it approaches 0 from the left, it travels towards negative infinity. As it approaches 0 from the right, it travels towards positive infinity. Therefore, the limit of the function as it approaches 0 does not exist.
The value of y as x changes depends on the function under consideration. The answer could be any of the following (or something quite different):y approaches a specific valuey approaches positive or negative infinityy is undefined
As x tends towards 0 (from >0), log(x) tend to - infinity. As x tends to + infinity so does log (x), though at a much slower rate.
f(t) = a + b*c-t, where a, b c are constants and t is a non-negative variable, is the general form of a function describing exponential decay. t is usually a variable related to time.The value of the function starts off f(0) = a + b and decreases (decays) towards f(t) = a.In some cases, such as radio active decay or a population extinction, a is zero so the amount of radioactive material left or surviving individuals decreases to zero.
Your question seems very confused. The normal convention of the Cartesian coordinate system would place negative numbers below the x axis, so that any curve approaching negative infinity would curve downward, not upward.
Yes, to the left (towards minus infinity).Yes, to the left (towards minus infinity).Yes, to the left (towards minus infinity).Yes, to the left (towards minus infinity).
If graphed in standard form (for example, x-axis is horizontal, with increasing values towards the right):The function value increases from left to right (it is strictly increasing monotonic).The function is concave upwards (its slope increases from left to right).It crosses the y-axis a y = 1.Values are always positive.Towards the left, values get closer and closer to zero, but never quite reach it (if x tends towards minus infinity, y tends towards zero).Towards the right, the function value is unbounded (if x tends towards plus infinity, y tends towards plus infinity).
When the limit as the function approaches from the left, doesn't equal the limit as the function approaches from the right. For example, let's look at the function 1/x as x approaches 0. As it approaches 0 from the left, it travels towards negative infinity. As it approaches 0 from the right, it travels towards positive infinity. Therefore, the limit of the function as it approaches 0 does not exist.
y = -ax2+ bx + c where a > 0 (coefficient of x2is NEGATIVE).
The value of y as x changes depends on the function under consideration. The answer could be any of the following (or something quite different):y approaches a specific valuey approaches positive or negative infinityy is undefined
YES!!!! However, y = x^(3) does not have a vertex , but an horizontal point at the origin. However, y = ax^(3) + bx^(2) + dx + c will have vertices , and they are found by differemntiating, and equating to zero.
The exponential function - if it has a positive exponent - will grow quickly towards positive values of "x". Actually, for small coefficients, it may also grow slowly at first, but it will grow all the time. At first sight, such a function can easily be confused with other growing (and quickly-growing) functions, such as a power function.
As x tends towards 0 (from >0), log(x) tend to - infinity. As x tends to + infinity so does log (x), though at a much slower rate.
The arrows at the ends of a number line indicate that the line extends forever in both directions (i.e. towards positive infinity and negative infinity)...since there is no largest or smallest real number.
f(t) = a + b*c-t, where a, b c are constants and t is a non-negative variable, is the general form of a function describing exponential decay. t is usually a variable related to time.The value of the function starts off f(0) = a + b and decreases (decays) towards f(t) = a.In some cases, such as radio active decay or a population extinction, a is zero so the amount of radioactive material left or surviving individuals decreases to zero.
it is a domain error when trying to take 0 to the -1 power, but other negative powers are still just 0 (the same as positive) I'm not sure why -1 isn't though.I guess that's what the calculator said. Taking zero to a negative one power (or any negative power) is the same as 1 divided by 0, which is undefined. You could say it's infinity, but the limit does not exist.If you approach from the right (positive side) you go towards positive infinity.If you approach from the left (negative side) you go towards negative infinity.