Exponential and Logarithmic Transformations

Transformations of Exponentials And logarithms

Rules for transforming Logarithmic functions

• adding inside the parenthesis (Ex: Log₃(x+5)) the function moves left

• Subtracting inside the parenthesis (Ex: Log₅(x-1)) the function moves right

• adding outside the parenthesis {Ex: Log₃(x)+3} the function moves up

• Subtracting outside the parenthesis {Ex: Log₂(x)-5} the function moves down

• Multiply number bigger than 1 Ex: 4log(x) = vertical stretch

• Multiply number between 1 and 0 Ex: $\frac{1}{6}$ log(x) = vertical compression

• Negative out front is a reflection over x -axis

Rules for transforming Exponential functions

• adding in the exponentn (Ex:  $3^{\left(x+2\right)}$  ) the function moves left

• Subtracting in the exponent (Ex:  $4^{\left(x-1\right)}$  ) the function moves right

• adding outside the exponent {Ex:  $5^x+2$  } the function moves up

• Subtracting outside the exponent {Ex:  $10^x-2$ } the function moves down

• Multiply number bigger than 1 Ex:  $4\left(3^x\right)$   = vertical stretch

• Multiply number between 1 and 0 Ex:  $\frac{1}{2}\left(6^x\right)$  = vertical compression

• Negative out front is a reflection over x -axis

Multiple Choice

Write the equation of the function f(x)=log₃x after the following transformations:

Translate 6 units left and 4 units up.

• g(x)=log₃(x+6)+4

• g(x)=log₃(x+4)-6

• g(x)=log₃(x-6)+4

• g(x)=3log(x+6)+4

Multiple Choice

What transformations have happened to y = 2^x if the new equation is
 y = -2^(x+3) -6

• It stayed the same
• flips, up 3, left 6
• flips, right 3, down 6
• flips, left 3, down 6

Multiple Choice

 If g(x) is a transformation of f(x), describe the transformation.

$$g\left(x\right)=\left(2\right)0.25^x$$  
$$f\left(x\right)=0.25^x$$  

• Horizontal stretch

• Horizontal compression

• Vertical stretch

• Vertical compression

Multiple Choice

Using the parent function y=3^x what would the graph of y=3^x+1 look like?

• Horizontal shift left one unit

• Horizontal shift right one unit

• Vertical shift up one unit

• Vertical shift down one unit

Multiple Choice

Describe the transformations of f(x)= -log₂(x+1)

• left 1

• left one & over the y-axis

• left one & over the x-axis

• right one & over the x axis