Transformations of functions: Vertical stretches

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

0/1
?
Intros
Lessons
  1. An Experiment to Study "Vertical Stretches"
    Sketch and compare: (y)=x2+2\left( y \right) = {x^2} + 2
    VS.
    (2y)=x2+2\left( {2y} \right) = {x^2} + 2
    VS.
    (y3)=x2+2\left( {\frac{y}{3}} \right) = {x^2} + 2
  2. a) Sketch all three quadratic functions on the same set of coordinate axes.
  3. Compared to the graph of (y)=x2+2\left( y \right) = {x^2} + 2:
    (2y)=x2+2\left( {2y} \right) = {x^2} + 2 is a vertical stretch about the x-axis by a factor of ____________.
    (y3)=x2+2\left( {\frac{y}{3}} \right) = {x^2} + 2 is a vertical stretch about the x-axis by a factor of ____________.
0/1
?
Examples
Lessons
  1. Vertical Stretches
    Given the graph of y=f(x)y = f\left( x \right) as shown, sketch:
    1. y=12f(x)y = \frac{1}{2}f\left( x \right)
    2. y=43f(x)y = \frac{4}{3}f\left( x \right)
    3. In conclusion:
      (y)(2y)\left( y \right) \to \left( {2y} \right): vertical stretch by a factor of ________ ⇒ all yy coordinates ______________________.
      (y)(34y)\left( y \right) \to \left( {\frac{3}{4}y} \right): vertical stretch by a factor of ________ ⇒ all yy coordinates ______________________.
      Vertical stretches in transformations