Transforming functions: vertical shifts

Now Playing:Transformations of functions vertical translations– Example 1

An Experiment to Study "Vertical Translations"

Sketch and compare: $\left( y \right) = {x^2}$
VS.
$\left( {y - 3} \right) = {x^2}$
VS.
$\left( {y + 2} \right) = {x^2}$
An Experiment to Study "Vertical Translations"

Sketch and compare: $\left( y \right) = {x^2}$
VS.
$\left( {y - 3} \right) = {x^2}$
VS.
$\left( {y + 2} \right) = {x^2}$
Sketch all three quadratic functions on the same set of coordinate axes.
An Experiment to Study "Vertical Translations"

Sketch and compare: $\left( y \right) = {x^2}$
VS.
$\left( {y - 3} \right) = {x^2}$
VS.
$\left( {y + 2} \right) = {x^2}$
Compared to the graph of $y = {x^2}$ :
• the graph of $\left( {y - 3} \right) = {x^2}$ is translated "vertically" ________ units _____________.
• the graph of $\left( {y + 2} \right) = {x^2}$ is translated "vertically" ________ units _____________.

Vertical Translations
Given the graph of $y=f(x)$ as shown, sketch:
1. $y = f\left( x \right) - 8$
2. $y = f\left( x \right) + 3$
3. In conclusion:
  • $\left( y \right) \to \left( {y + 8} \right)$ : shift ________ units ______________ $\Rightarrow$ all $y$ coordinates _____________________________.
  • $\left( y \right) \to \left( {y - 3} \right)$ : shift ________ units ______________ $\Rightarrow$ all $y$ coordinates _____________________________.