math 4.1-4.5

$$f(x) = a^x + c$$

Vertical shift

$f(x) = a^{x - c}$ ($c > 0$)

Horizontal shift righ

f(x)=a^x-c

Horizontal shift right

f(x)=(a^x)+c

Vertical shift down

f(x)=-a^x

Reflection on the x-axis

$$f(x) = a^{-x}$$

Reflection of $f(x) = a^x$ across the $y$-axis

$f(x) = c a^x$ ($c > 1$)

Vertical stretch by a factor of $c$

Transformation represented by $f(x) = c a^x$ when $0 < c < 1$

Vertical shrink