## How do you translate logarithmic functions?

The logarithmic function, y=logb(x) , can be shifted k units vertically and h units horizontally with the equation y=logb(x+h)+k . If k>0 , the graph would be shifted upwards. If k<0 , the graph would be shifted downwards. If h>0 , the graph would be shifted left.

## What is the domain of a transformed logarithmic function?

The domain of a transformed logarithmic function is always {x ∈ R}.

**What are the transformations of exponential functions?**

Transformations of exponential graphs behave similarly to those of other functions. Just as with other parent functions, we can apply the four types of transformations—shifts, reflections, stretches, and compressions—to the parent function f(x)=bx f ( x ) = b x without loss of shape.

### What are logarithmic functions?

Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay. The logarithmic function y = logax is defined to be equivalent to the exponential equation x = ay. This unknown exponent, y, equals logax.

### How do you tell if a logarithmic function is increasing or decreasing?

State the domain, range, and asymptote. Before graphing, identify the behavior and key points for the graph. Since b = 5 is greater than one, we know the function is increasing. The left tail of the graph will approach the vertical asymptote x = 0, and the right tail will increase slowly without bound.

**How to solve logarithmic functions?**

Simplify the logarithmic equations by applying the appropriate laws of logarithms.

## How to graph logarithmic functions?

Since all logarithmic functions pass through the point (1, 0), we locate and place a dot at the point.

## Why are logarithmic functions used?

Logarithmic functions are used to simplify complex calculations in many fields, including statistics, engineering, chemistry, physics, and music. For example, and are logarithmic functions that essentially simplify multiplication to addition and division to subtraction.