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Sec 7 7 transformations on exp log functions answers

Sec 7 7 transformations on exp log functions answers 2025

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The document discusses transformations of exponential and logarithmic functions, detailing vertical and horizontal translations, vertical stretches/compressions, and reflections across the x-axis. It provides examples of each transformation type with specific equations and instructions for sketching graphs using tables of values to illustrate these transformations.

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What are the transformations of a logarithmic function?

Summarizing Transformations of Logarithmic Functions Transformations of the Parent Function y=logb(x)TranslationFormReflection about the x-axisy=logb(x)Reflection about the y-axisy=logb(x)General equation for all transformationsy=alogb(x+c)+d2 more rows

How do you translate a log function?

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 k0 , the graph would be shifted upwards. If k0 , the graph would be shifted left.

What is the logarithmic parent function?

Instruction: The logarithmic parent function is f(x) = logb x, b 0 and b 1, where the base b is a constant and the x is the independent variable.

How to do a stretch on a graph?

Multiplying the x by a number between 0 and 1 will make the graph wider, or stretched horizontally. For example, multiplying the input by 2 would produce a graph that is half as wide. But multiplying the input by 0.5 results in a graph that is twice as wide, or stretched horizontally .

How do you compress a log function?

VERTICAL STRETCHES AND COMPRESSIONS OF THE PARENT FUNCTION Y=LOGB(X) stretches the parent function y=logb(x) vertically by a factor of a if a1. compresses the parent function y=logb(x) vertically by a factor of a if 0

How do you find the vertical stretch of a log function?

Vertical Stretches and Compressions To visualize stretches and compressions, we set a1 and observe the general graph of the parent function f(x)=logb(x) alongside the vertical stretch, g(x)=alogb(x) and the vertical compression, h(x)=1alogb(x).

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