What are the transformations of an exponential function?
Our basic exponential function is f(x) = b^x, where b is our base, which is a positive constant. All other exponential functions are modifications to this basic form. Transformations are changes to the graph. Transformations include vertical shifts, horizontal shifts, and graph reversals.
What are the transformations of a logarithmic function?
8.2- Transformations of Logarithmic Functions
| Transformation | Function notation |
|---|---|
| Horizontal translation | f(x-d) |
| Vertical compression Vertical stretch | af(x) |
| Horizontal compression Horizontal stretch | f((1/k)x) |
| Reflection across y-axis Reflection across x-axis | -f(x) f(x) |
What are some examples of exponential functions?
The examples of exponential functions are:
- f(x) = 2. x
- f(x) = 1/ 2x = 2. -x
- f(x) = 2. x+3
- f(x) = 0.5. x
What are the examples of exponential equation?
An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3x = 81, 5x – 3 = 625, 62y – 7 = 121, etc are some examples of exponential equations.
How do you solve exponential and logarithmic equations?
To solve an exponential equation, first isolate the exponential expression, then take the logarithm of both sides of the equation and solve for the variable. 2. To solve a logarithmic equation, first isolate the logarithmic expression, then exponentiate both sides of the equation and solve for the variable.
What is exponential and logarithmic functions?
An exponential function has the form ax, where a is a constant; examples are 2x, 10x, ex. The logarithmic functions are the inverses of the exponential functions, that is, functions that “undo” the exponential functions, just as, for example, the cube root function “undoes” the cube function: 3√23=2.
What is logarithmic equation with example?
| LOGARITHMIC EQUATIONS | |
|---|---|
| Definition | Any equation in the variable x that contains a logarithm is called a logarithmic equation. |
| Recall the definition of a logarithm. This definition will be important to understand in order to be able to solve logarithmic equations. | |
| Examples | EXAMPLES OF LOGARITHMIC EQUATIONS |
| Log2 x = -5 |
What is an example of exponential function?
Exponential Functions Examples The examples of exponential functions are: f(x) = 2. f(x) = 1/ 2x = 2. f(x) = 2.
What is exponential form examples?
The exponential form is an easier way of writing repeated multiplication involving base and exponents. For example, we can write 5 × 5 × 5 × 5 as 54 in the exponential form, where 5 is the base and 4 is the power. In this form, the power represents the number of times we are multiplying the base by itself.
How do you transform graphs of exponential and logarithmic functions?
You can transform graphs of exponential and logarithmic functions in the same way you transformed graphs of functions in previous chapters. Examples of transformations of the graph of f ( x) = 4x are shown below.
How to represent the logarithmic function with the inverse of exponential function?
If the inverse of the exponential function exists then we can represent the logarithmic function as given below: Suppose b > 1 is a real number such that the logarithm of a to base b is x if b x = a. The logarithm of a to base b can be written as log b a. Thus, log b a = x if b x = a.
What is the transformation of logarithmic functions?
The transformation of functions includes the shifting, stretching, and reflecting of their graph. The same rules apply when transforming logarithmic and exponential functions. Suppose c > 0.
What is an example of an exponential function?
Exponential functions are equations with a base number (greater than one) and a variable, usually {eq}x {/eq}, as the exponent. Here is an example of an exponential function: {eq}y=2^x {/eq}.