Graph the following equation.   y = 2(f(x))

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Hi, Kristen,

What Embizze has is absolutely correct.  I wanted to add, it's a dilation as in, it gets stretched from the x axis.  So, for example, the graph of y = 3x:

It would be the black line.  But, then, multiply f(x) by 2, so:

y = 3x --> y = 2*3x = 6x

The new graph becomes:

The new graph is in red.  As the perspective is, one talks of how each point gets moved away from the x axis further.  It goes up above the x axis and down below the x axis.  All the same with the quadratic curve Embizze showed.

Good luck, Kristen.  I hope this helps.

Till Then,


Steve

Approved by eNotes Editorial Team
An illustration of the letter 'A' in a speech bubbles

If you are given f(x) and you are asked to graph y=2(f(x)):

Note that the type of graph will not change. So a line remains a line, a parabola remains a parabola, etc... Multiplying by 2 is a dilation (stretch) of factor 2.

You can build a table with the following headings: x ; f(x) ; 2f(x) and plot the points.

Alternatively, you can graph y=f(x) and then take each y-value and double it to form the graph of y=2f(x).

For example, if `y=x^2` then you have, among others, the points (-2,4),(-1,1),(0,0),(1,1),(2,4). The function `y=2f(x)=2x^2` has the following points: (-2,8),(-1,2),(0,0),(1,2),(2,8)

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial