0
What else can I help you with?
Give an example of a relation that is a function but whose inverse is not a function?
An example of a relation that is a function but whose inverse is not a function is the relation defined by the equation ( f(x) = x^2 ) for ( x \geq 0 ). This function maps each non-negative ( x ) to a non-negative ( y ), making it a valid function. However, its inverse, ( f^{-1}(y) = \sqrt{y} ), does not satisfy the definition of a function when considering the entire range of ( y ) values (since both positive and negative values of ( y ) yield the same ( x )). Thus, the inverse is not a function.
Which the function's values become very positive or negative numbers?
The positive regions of a function are those intervals where the function is above the x-axis. It is where the y-values are positive (not zero). The negative regions of a function are those intervals where the function is below the x-axis. It is where the y-values are negative (not zero).
Why negative value is not valid for log?
The logarithm function is the inverse of the exponential function. Take the exponential function (base 10): y = 10x. The inverse of this is x = 10y. The function y = log(x) is used to define this inverse function. First look at y = 10x. Any real value of x will yield a positive real value for y. If x = 0, then y = 1; if x < 0 (negative) then y is between 0 and 1 (it will never equal zero, though). A value of 10-99999 is very close to zero, but not quite there. There are no real values of x which will give a negative y value for y = 10x. Now look at y = log(x) or x = 10y. No matter what real values for y, that we choose, x will always be a positive number, so a negative value of x in y = log(x) is not possible if you are limiting to real numbers. It is possible with complex and imaginary numbers to take a log of a negative number, or to get a negative answer to y = 10x.
Give an example of a relation that is NOT a function and explain why it is not a function?
y² = x --> y = ±√x Because there are *two* square roots for any positive number (positive and negative) this will not be a function.
What does a negative minus a negative equal?
Suppose x and y are two POSITIVE numbers so that -x and -y are negative. Then a negative minus a negative = (-x) - (-y) = -x +y If x > y the answer is negative If x = y the answer is zero If x < y the answer is positive
Give an example of a relation that is a function but whose inverse is not a function?
An example of a relation that is a function but whose inverse is not a function is the relation defined by the equation ( f(x) = x^2 ) for ( x \geq 0 ). This function maps each non-negative ( x ) to a non-negative ( y ), making it a valid function. However, its inverse, ( f^{-1}(y) = \sqrt{y} ), does not satisfy the definition of a function when considering the entire range of ( y ) values (since both positive and negative values of ( y ) yield the same ( x )). Thus, the inverse is not a function.
Which the function's values become very positive or negative numbers?
The positive regions of a function are those intervals where the function is above the x-axis. It is where the y-values are positive (not zero). The negative regions of a function are those intervals where the function is below the x-axis. It is where the y-values are negative (not zero).
Why negative value is not valid for log?
The logarithm function is the inverse of the exponential function. Take the exponential function (base 10): y = 10x. The inverse of this is x = 10y. The function y = log(x) is used to define this inverse function. First look at y = 10x. Any real value of x will yield a positive real value for y. If x = 0, then y = 1; if x < 0 (negative) then y is between 0 and 1 (it will never equal zero, though). A value of 10-99999 is very close to zero, but not quite there. There are no real values of x which will give a negative y value for y = 10x. Now look at y = log(x) or x = 10y. No matter what real values for y, that we choose, x will always be a positive number, so a negative value of x in y = log(x) is not possible if you are limiting to real numbers. It is possible with complex and imaginary numbers to take a log of a negative number, or to get a negative answer to y = 10x.
Give an example of a relation that is NOT a function and explain why it is not a function?
y² = x --> y = ±√x Because there are *two* square roots for any positive number (positive and negative) this will not be a function.
What does a negative minus a negative equal?
Suppose x and y are two POSITIVE numbers so that -x and -y are negative. Then a negative minus a negative = (-x) - (-y) = -x +y If x > y the answer is negative If x = y the answer is zero If x < y the answer is positive
Does the equation define y as a function of x x equals y squared?
It depends on the domain of y. If that is restricted to non-negative values, then the answer is yes. But if y is allowed to be negative, then the answer is no because then there are two values of y for each non-zero value of x.
What is the end behavior of a function?
The end behavior of a function is how the function acts as it approaches infinity and negative infinity. All even functions such as x^2 approach infinity in the y-axis as x approaches infinity and odd functions such as x^3 approach positive infinity in the y- axis as x approaches positive infinity and negative infinity in the y- axis as x approaches negative infinity. If their is a negative leading coefficient then it is just flipped.
How do you figure out the intervals of increasing and decreasing of the function y equals x divided by square root of x squared then plus one?
The intervals are determined by when the derivative is positive or negative, because the derivative is the slope and a negative slope means the function is decreasing. The function y=(x/sqrt(x2))+1, however, can be rewritten as y=x/absolutevalue(x) + 1, and as such will be represented as a pair of parallel lines, y=0 for x<0 and y=2 for x>0. As the lines are horizontal, the function is never increasing or decreasing.
What does function of x equals function of -x mean?
It means that the value of the function at any point "x" is the same as the value of the function at the negative of "x". The graph of the function is thus symmetrical around the y-axis. Examples of such functions are the absolute value, the cosine function, and the function defined by y = x2.
How will the y value be different if x is negative or positive?
The y value will differ based on the relationship defined in the function or equation involving x. If the function is linear, for example, a positive x might yield a higher y value than a negative x, reflecting the slope's direction. In nonlinear functions, the difference can be more complex, with y values potentially changing dramatically depending on the specific equation. Therefore, the effect of x being negative or positive on y depends on the nature of the function being analyzed.
What is a positive or negative relationship on a graph?
If a function Y is dependent on X. if X increases in value then Y also increases then we call this a positive relationship. If X increases in value then Y decreases or vice versa then we call this a negative relationship.
What happens to the y-value of the function after the graph crosses the x-axis?
When the graph of a function crosses the x-axis, the y-value of the function changes from positive to negative or vice versa. Specifically, at the point where the graph crosses the x-axis, the y-value is zero. After crossing, if the graph continues upward, the y-value becomes positive; if it continues downward, the y-value becomes negative. This behavior indicates a change in the function's output relative to the x-axis.
