# FNGR 1 | Lesson 4 | Explore (Horizontal Translations)

## Horizontal Translations

A horizontal transformation occurs when we add or subtract a constant value to the inputs. It is represented as either $$f(x+h)$$ or $$f(x-h)$$.

Example:

The parent function for the exponential is $$f(x)=2^x$$:

If we translate this graph left 4 units we end up with this graph:

The new equation for the function is $$f(x)=2^{(x+4)}$$.

Examine the table of values for the original and the new functions:

$$x$$ $$f(x)=2^x$$
$$-2$$ $$\dfrac{1}{4}$$
$$-1$$ $$\dfrac{1}{2}$$
$$0$$ $$1$$
$$1$$ $$2$$
$$2$$ $$4$$
$$x$$j0 $$f(x)=2^{(x+4)}$$
$$-6$$ $$\dfrac{1}{4}$$
$$-5$$ $$\dfrac{1}{2}$$
$$-4$$ $$1$$
$$-3$$ $$2$$
$$-2$$ $$4$$

What do you notice? What do you wonder? Describe what you think is happening in your own words. How does this compare to the graphs above?