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

steveschoen | College Teacher | (Level 1) Associate Educator

Posted on

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

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

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)