Exponential Functions: Characteristics, Transformations, and Examples, Study notes of Algebra

Download Exponential Functions: Characteristics, Transformations, and Examples and more Study notes Algebra in PDF only on Docsity!

Math 1310Chapter 5 – Section 5.1Exponential Functions

Exponential Function with base

b For^ b^ > 0, a function^ f^ of the form

is called the^ exponential function with base

b. Characteristics of Exponential Functionsof the form • The graphs of all exponential functions of the form^

pass through the key point (0, 1).• The^ x -axis ( y^ = 0) is the horizontal asymptote.• The domain is all real numbers and the range is

xbxf =)(^ xbxf =)(^ xbxf^ =)( ).,^0 (^ ∞

If 0 <^ b^ < 1 then the graph of

looks

like:^

y

x bxf =)( x

Example 1: Graph the following pair of functions on the same set of axes.^ x^1 ⎞⎛ x ,^2 )(^ xf^ = xg^ =^ )(⎟⎜^2 ⎠⎝

Recommended Order for Transformations of Functions 1. Vertical Stretching or Vertical Shrinking2. Reflection in the^ x -axis3. Horizontal and Vertical Translations4. Reflection in the^ y -axis

Example 2: Apply transformations to sketch the graph of the following function. Show theasymptote and then state the domain and range of the function.^1 − x^12 )(^ +=^ xf Example 3: Apply transformations to sketch the graph of the following function. Show theasymptote and then state the domain and range of the function.^ x^1 ⎞⎛^1 )(^ −−= xf ⎟⎜^3 ⎠⎝