Respuesta :
Remember the following transformations of a function:
[tex]c\cdot f(x)[/tex]This transformation stretches the function over the vertical axis if c>1 and shrinks it if 0
If c is positive, the orientation is mantained, and if c is negative, the function is also flipped over (it shrinks if -1
[tex]f(x)+c[/tex]This transformation moves the function vertically c units. It goes up if c>0 and down if c<0.
Therefore, starting with the absolute value function:
[tex]\lvert x\rvert[/tex]Multiply the function by 2:
[tex]2\cdot\lvert x\rvert[/tex]Since 2>1, then this is a vertical stretching by a factor of 2.
Next, add 1:
[tex]2\cdot\lvert x\rvert+1[/tex]This will translate the stretched absolute value function one unit upwards.
Therefore, the complete description of the transfromation would be:
[tex]y=2\cdot\lvert x\rvert+1[/tex]Is a vertical stretching of the absolute value function by a factor of 2, translated 1 unit upwards.
