The types of transformations that are used to transform linear and absolute value functions, can also be applied to exponential functions in the same way. The way transformations affect graphs is independent of what type of graph is being transformed. Thus, even though exponential functions are fundamentally different from linear ones, they are affected similarly by these transformations. By adding some number to every function value, a function graph is translated vertically. Notice that since the resulting function has a constant term, it can't be written in the form $g(x)=a\cdot b^x.$ Thus, $g$ is not an exponential function. This is the only of the following transformations that changes an exponential function into something other than an exponential function. A graph is translated horizontally by subtracting a number from the input of the function rule. Note that the number, $h,$ is subtracted and not added — a positive $h$ translates the graph to the right. A function is reflected in the $x$-axis by changing the sign of all function values: Graphically, all points on the graph move to the opposite side of the $x$-axis, while maintaining their distance to the $x\text{-}$axis. A graph is instead reflected in the $y$-axis, moving all points on the graph to the opposite side of the $y$-axis, by changing the sign of the input of the function. Note that the $y\text{-}$intercept is preserved. A function graph is vertically stretched or shrunk by multiplying the function rule by some constant $a>0$: All vertical distances from the graph to the $x$-axis are changed by the factor $a.$ Thus, preserving any $x\text{-}$intercepts. By instead multiplying the input of a function rule by some constant $a>0,$ its graph will be horizontally stretched or shrunk by the factor $\frac{1}{a}.$ Since the $x$-value of $y\text{-}$intercepts is $0,$ they are not affected by this transformation.