Transformations of Exponentials And logarithms

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

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