Chapter Closure
Sign In
Add 2 to the given function.
Multiply the given function by 2.
Calculate the function's value with an argument of x+2.
Calculate the function's value with an argument of 2x.
Expression: 2x^2+2
New Graph's Description: Shifted 2 units up
Expression: 4x^2
New Graph's Description: Stretched vertically by a factor of 2
Expression: 2(x+2)^2
New Graph's Description: Shifted 2 units left
Expression: 8x^2
New Graph's Description: Stretched horizontally by a factor of 2
Using the function f(x), we want to find the expression f(x)+2. To do this, we will add 2 to the given function.
Now, let's look at all of the possible transformations so that we can more clearly identify what is happening to our function.
| Transformations of f(x) | |
|---|---|
| Vertical Translations | Translation up k units, k>0 y=f(x)+ k |
| Translation down k units, k>0 y=f(x)- k | |
| Horizontal Translations | Translation right h units, h>0 y=f(x- h) |
| Translation left h units, h>0 y=f(x+ h) | |
| Vertical Stretch or Compression | Vertical stretch, a>1 y= af(x) |
| Vertical compression, 0< a< 1 y= af(x) | |
| Horizontal Stretch or Compression | Horizontal stretch, 0< b<1 y=f( bx) |
| Horizontal compression, b>1 y=f( bx) | |
| Reflections | In the x-axis y=- f(x) |
| In the y-axis y=f(- x) | |
As we can see, we can describe this transformation as a vertical translation 2 units up. It means that the graph of the given function was shifted 2 units up.
Using the function f(x), we want to find the expression 2 * f(x). To do this, we will multiply the given function by 2 and simplify.
We can describe this transformation as a vertical stretch by a factor of 2.
Using the function f(x), we want to evaluate for the given value, f( x+2). To do this we need to substitute x+2 for x in each instance of the x-variable.
We can describe this transformation as a horizontal translation 2 units left. It means that the graph of the given function was shifted 2 units left.
Using the function f(x), we want to evaluate for the given value, f( 2x). To do this we need to substitute 2x for x in each instance of the x-variable and simplify.
x= 2x
(a * b)^m=a^m* b^m
Calculate power
Multiply
We can describe this transformation as a horizontal stretch by a factor of 2.