Can a function have a negative x value?

Recall that x can never be negative here because the square root of a negative number would be imaginary, and imaginary numbers cannot be graphed. There are also no values for x that will result in y being a negative number.

Can an output of a function be negative?

We can also reflect the graph of a function over the x-axis (y = 0), the y-axis(x = 0), or the line y = x. Making the output negative reflects the graph over the x-axis, or the line y = 0.

How do you determine whether a function is even odd or neither?

Answer: For an even function, f(-x) = f(x), for all x, for an odd function f(-x) = -f(x), for all x. If f(x) ≠ f(−x) and −f(x) ≠ f(−x) for some values of x, then f is neither even nor odd. Let’s understand the solution.

What happens when the exponent is negative 1?

A negative exponent takes us to the inverse of the number. In other words, a-n = 1/an and 5-3 becomes 1/53 = 1/125. This is how negative exponents change the numbers to fractions. Let us take another example to see how negative exponents change to fractions.

What does it mean for a function to be negative?

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). • y-values that are on the x-axis are neither positive nor negative.

Can functions be zero?

A zero function is a constant function for which the output value is always zero irrespective of the inputs.

Can zero be a range?

The range is also all real numbers except zero.

What is the only function that is both even and odd?

f(x) = 0
The only function which is both even and odd is f(x) = 0, defined for all real numbers. This is just a line which sits on the x-axis. If you count equations which are not a function in terms of y, then x=0 would also be both even and odd, and is just a line on the y-axis.

Are linear functions even or odd?

This linear function is symmetric about the origin and is an odd function: \begin{align*}f(x)=f(-x)\end{align*}. As shown earlier in the concept, this quadratic function is symmetric about the \begin{align*}y\end{align*}-axis and is an even function: \begin{align*}f(x)=f(-x)\end{align*}.

Is there such thing as a negative exponent?

A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ. For example, 2⁻⁴ = 1 / (2⁴) = 1/16.

Is it difficult to raise a number to an irrational power?

Answer Wiki. Raising a number to an irrational power is no more complicated, in principle, than multiplying a number by an irrational number or, for that matter, multiplying a number by a non-integer rational number.

How do you multiply a natural number to an irrational number?

Multiplying a natural number by a natural number has a natural meaning 🙂 As soon as you go to multiplying a number by a rational number, say p q you have to extend the meaning. Thus: n × p q ≡ n × p q by definition. Raising numbers to an irrational power requires a similar extension of the natural meaning of exponentiation. Thus

Do the laws of exponents work for integer powers?

After a while, we can show, more or less rigorously, that the laws of exponentsthat worked for integer powers also work for expressions of the form $x^{p/q}$, where $p$ and $q$ are integers. However, what do we mean, for example, by $3^{\\sqrt{2}}$?

Can we construct a sequence of rational numbers whose limit is π?

In fact, we may construct a sequence of rational numbers whose limit is a given irrational number. For instance, consider the sequence: 3, 31/10, 314/100, 3141/1000, 31415/10000, etc. This is an increasing sequence of rational numbers that converge to π. Others have mentioned logarithms, but that doesn’t completely answer the question.