Exponential and Logarithmic Functions

Questions and Answers

What is the definition of an exponential function?

log b of a = log of a/log of b

f(n) = aⁿ, where a is constant (correct)

log base of # = exponent

f(x) = log of x

What is always true about the range of exponential functions?

The range is always positive.

What is the first step in graphing exponential functions?

Connect the line

Make a table by plugging in coordinates for x (correct)

Plot points

Flip the table

What is the process to graph logarithmic functions?

Switch x and y coordinates Signup and view all the answers

What does 'logarithm' entail regarding negative numbers?

It is not possible to take the log of a negative number. Signup and view all the answers

What is the change of base formula?

log b of a = log of a/log of b Signup and view all the answers

What is the parent log graph equation?

f(x) = log of x Signup and view all the answers

What transformation does f(x) = a + log of (x-b) indicate?

Shifts up by a units. Signup and view all the answers

Study Notes

Exponential Functions

Defined as f(n) = aⁿ, where "a" is a constant.
Range is always positive; approaches zero but never reaches it as the domain decreases.

Graphing Exponential Functions

Create a table by inputting values for x.
Plot corresponding points on the graph.
Connect points to form a smooth curve representing the function.

Graphing Logarithmic Functions

Determine the inverse of the log function, which is an exponential function.
Input values for x into a table and calculate corresponding y values.
Switch the x and y coordinates to invert the table.
Plot the new points and connect them to visualize the logarithmic function.

Logarithm

Represents the relationship log base of a number equals the exponent.
Taking the logarithm of negative numbers is not permissible; the argument must always be positive.

Change of Base Formula

Provides a method for calculating logarithms with different bases.
Expressed as log b of a = log of a / log of b.

Parent Log Graph

The basic log function is defined as f(x) = log of x.
Serves as the foundational graph for logarithmic transformations.

Logarithmic Transformations

Generally expressed as f(x) = a + log of (x-b).
The "a" value determines vertical shifts, moving the graph up by "a" units.

Description

This quiz covers the concepts of exponential and logarithmic functions, including definitions, graphing techniques, and the change of base formula. Test your understanding of how these functions relate and how to visualize them effectively with tables and graphs.