Algebra 2 Notes



Algebra 2 Notes Name: ________________

Section 7.7 – Transforming Exponential and Log Functions

You can perform the same transformations on exponential functions that you performed on polynomial, quadratic, and linear functions.

|Transformations of Exponential Functions |

|Transformation |[pic] Notation |Examples |

| |[pic] |[pic] _________________________ |

|Vertical translation | |[pic] _________________________ |

| |[pic] |[pic] _________________________ |

|Horizontal translation | |[pic] _________________________ |

| |[pic] |[pic] _________________________ |

|Vertical stretch or compression | |[pic] _________________________ |

| |[pic] |[pic] _________________________ |

|Horizontal stretch or compression | |[pic] _________________________ |

| |[pic] |[pic] _________________________ |

|Reflection |[pic] |[pic] _________________________ |

Example 1: Graph each function. Find the asymptote, state the domain and range, and describe the transformation on the parent function. Also find the [pic]-intercept.

|a. [pic] |b. [pic] |c. [pic] |

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| |[pic] | |

| | |[pic] |

|[pic] | | |

Example 2: Write the equation for each of the following…

|a. [pic] translated 3 units left and compressed vertically by a factor of |b. [pic] reflected across the [pic]-axis and translated 6 units up |

|[pic] | |

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|c. [pic] stretched vertically by a factor of 3 and translated 1 unit right |d. [pic] translated 5 units down and reflected across the [pic]-axis |

|and 4 units up | |

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Because a log is an exponent, transformations of logarithmic functions are similar to transformations of exponential functions. You can stretch, reflect, and translate the graph of the parent function [pic]. Examples are given below for [pic].

|Transformations of Logarithmic Functions |

|Transformation |[pic] Notation |Examples |

| |[pic] |[pic] _______________________ |

|Vertical translation | |[pic] _______________________ |

| |[pic] |[pic] ______________________ |

|Horizontal translation | |[pic] ______________________ |

| |[pic] |[pic] ________________________ |

|Vertical stretch or compression | |[pic] ________________________ |

| |[pic] |[pic] ______________________ |

|Horizontal stretch or compression | |[pic] ______________________ |

| |[pic] |[pic] _______________________ |

|Reflection |[pic] |[pic] _______________________ |

Example 3: Graph each function. Find the asymptote, state the domain and range, and describe the transformation on the parent function. Also find the [pic]-intercept.

|a. [pic] |b. [pic] |c. [pic] |

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|[pic] | | |

| |[pic] |[pic] |

Example 4: Write the equation for each of the following…

|a. [pic] translated 2 units right and reflected across the [pic]-axis |b. [pic] stretched vertically by a factor of [pic] and translated 5 units |

| |left |

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|c. [pic] reflected across the [pic]-axis and stretched horizontally by a |d. [pic] compressed vertically by a factor of [pic] and translated 3 units |

|factor of 4 |right and 6 units down |

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