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Cycle 1 - Lesson 9 – Exponential and Logarithmic Functions If the growth of a population is proportional to the size of the population as it grows, we describe the growth as EXPONENTIAL. Bacterial growth and compound interest are examples of exponential growth. Exponential decay occurs in nuclear reactions and in the depreciation in value of vehicles. In this lesson, we will review how to graph an exponential function and its inverse. The inverse of a function is when the x and y values switch, and on graph this is a reflection in the line y = x.

Desmos Investigation #1 – Reviewing the basic exponential function Make a table of values and sketch a graph of the function

x

y

Δy

-3 -2 -1 -0.5 0 0.5 1 2 3 Horizontal asymptote:

Vertical asymptote:

x-intercepts:

y-intercept:

Domain:

Range:

End behaviour: as x +∞

as x-∞

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Desmos Investigation #2 – The Exponential function and its Inverse (the logarithmic) Graph the functions below on Desmos at the same time and draw sketches on the grids.

Domain:

Domain:

Range:

Range:

Asymptote:

Asymptote:

Intercepts:

Intercepts:

What kind of transformation to the exponential function will result in the logarithmic function? ___________________________________________________________________ Desmos Investigation #3 – Using sliders to explore the exponential and its inverse

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Cycle 1 – Lesson 9 - PRACTICE QUESTIONS – Part I

ANSWERS

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Cycle 1 – Lesson 9 - PART II – The Logarithm

Examples

c) log 0.01

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Cycle 1 – Lesson 9 - PRACTICE QUESTIONS – Part II

ANSWERS