Is a exponential function a one-to-one?

Is a exponential function a one-to-one?

Exponential functions are one-to-one functions. The parent function, y = bx, will always have a y-intercept of one, occurring at the ordered pair of (0,1). Algebraically speaking, when x = 0, we have y = b0 which is always equal to 1.

How do you find the properties of an exponential function?

Exponential Function Rules

1. ax ay = a. x+y
2. ax/ay = a. x-y
3. (ax)y = a. xy
4. axbx=(ab) x
5. (a/b)x= ax/b. x
6. a0=1.
7. a-x= 1/ a. x

How do you solve a one-to-one property?

Method 1: One-to-One Property

1. Rewrite both sides of the equation as an exponential expression with the same base. If this cannot be done, use method 2.
2. Since the bases are equal, then the exponents must be equal. Set the exponents equal to each other and solve.
3. Check your solution.

What is a one to one function example?

A one-to-one function is a function of which the answers never repeat. For example, the function f(x) = x + 1 is a one-to-one function because it produces a different answer for every input. An easy way to test whether a function is one-to-one or not is to apply the horizontal line test to its graph.

What are properties of exponential?

Exponential Properties: 1. Product of like bases: To multiply powers with the same base, add the exponents and keep the common base. Power to a power: To raise a power to a power, keep the base and multiply the exponents. 4. Product to a power: To raise a product to a power, raise each factor to the power.

What are 3 properties of an exponential function?

decay, exponent rules (like the product and quotient rules), and rate of change (which is proportional to the y-values).

What is exponential calculator?

In addition to these keys, scientific calculators usually have two keys for exponential functions: Exponent: The key denoted by ^ or by capital E raises ay number to any exponent. Natural Exponent: The key, denoted by ex, raises e to the power you enter.

How are exponents multiplied in an exponent calculator?

When exponents are raised to another exponent, the exponents are multiplied. (a m) n = a (m × n) EX: (2 2) 4 = 4 4 = 256 (2 2) 4 = 2 (2 × 4) = 2 8 = 256 When multiplied bases are raised to an exponent, the exponent is distributed to both bases.

Which is the only way for an exponent to remain unchanged?

Thus, the only way for an to remain unchanged by multiplication, and this exponent law to remain true, is for a 0 to be 1. When an exponent is a fraction where the numerator is 1, the n th root of the base is taken. Shown below is an example with a fractional exponent where the numerator is not 1.

When does the exponent of a fraction remain true?

If a n × a m = a (n+m) Then a n × a 0 = a (n+0) = a n. Thus, the only way for an to remain unchanged by multiplication, and this exponent law to remain true, is for a 0 to be 1. When an exponent is a fraction where the numerator is 1, the n th root of the base is taken.

Can you use an exponent calculator with negative bases?

The calculator above accepts negative bases, but does not compute imaginary numbers. It also does not accept fractions, but can be used to compute fractional exponents, as long as the exponents are input in their decimal form. When exponents that share the same base are multiplied, the exponents are added.