Sign In | Starter Of The Day | Tablesmaster | Fun Maths | Maths Map | Topics | More

International Baccalaureate Mathematics

Functions

Syllabus Content

Exponential functions and their graphs: f(x)=ax, a>0, f(x)=ex. Logarithmic functions and their graphs: f(x)=logax, x>0, f(x)=lnx, x>0

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

Here are some exam-style questions on this statement:

See all these questions

Click on a topic below for suggested lesson Starters, resources and activities from Transum.


Furthermore

Official Guidance, clarification and syllabus links:

Link to: financial applications of geometric sequences and series (SL 1.4).

Relationships between these functions: \(a^x=e^{x\ln{a}}; \quad \log_aa^x=x, \text{ where } a \gt 0, x \gt 0, a\neq 1 \)

Exponential and logarithmic functions as inverses of each other.

Formula Booklet:

Exponential and logarithmic functions

\(a^x=e^{x\ln{a}}; \quad \log_aa^x=x=a^{\log_ax}, \\ \text{ where } a \gt 0, x \gt 0, a\neq 1 \)

Exponential functions, represented as \( f(x) = a \cdot b^x \), where \( a \) and \( b \) are constants, exhibit a rapid increase or decrease as the value of \( x \) changes. The base \( b \) is a positive real number, and when \( b > 1 \), the function shows exponential growth, whereas if \( 0 < b < 1 \), it demonstrates exponential decay. The graph of an exponential function is a curve that either increases or decreases rapidly, but never crosses the x-axis, as it asymptotically approaches the axis. The general form of an exponential function is $$ f(x) = a \cdot b^x, $$ where \( a \) is the initial value, and \( b \) is the base of the exponential.

Logarithmic functions are the inverses of exponential functions. The logarithmic function \( g(x) = \log_b(x) \) is defined such that if \( y = \log_b(x) \), then the equivalent exponential expression is \( x = b^y \). The base \( b \) of the logarithm is the same as the base of the corresponding exponential function. Graphs of logarithmic functions are the reflection of their exponential counterparts across the line \( y = x \). The general form of a logarithmic function is $$ g(x) = \log_b(x), $$ where \( b \) is the base of the logarithm. Logarithmic functions are useful in solving equations where the variable is an exponent in an exponential function.

This video on Exponential and Logarithmic Functions is from Revision Village and is aimed at students taking the IB Maths AA SL/HL course

How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.


Apple

©1997-2024 WWW.TRANSUM.ORG