translations
To move a graph up 4 units, you add 4 to this part of the function.
What is the outside (or the \(y\)-value)?
This is where you put a negative sign to flip a graph over the (x)-axis.
front of the function
Multiplying a function by a number like 5 causes this type of vertical change
vertical stretch
inf(x - 1) + 8$, the graph moves right 1 and this many units up.
8
This is the direction the graph of f (x + 6) moves
What is left?
A negative sign inside the parentheses, like f (-x), flips the graph over this axis.
y-axis
To "shrink" or "compress" a graph vertically, you multiply the function by a number in this range.
between 0 and 1 (a fraction)
to graph -f(x) -2 you flip the graph over the x axis and then move it in this direction.
down
If you want to move a graph 3 units down, you subtract 3 from this
What is the entire function (or f (x)?
when you reflect (5,2) over the x axis this coordinate changes its sign.
What is the (y)-coordinate (becomes -2)
A vertical stretch by 2 would move the point (2, 3) to this new point
(2,6)
For the function 3f(x) + 1), you first stretch the graph by 3, then move it here.
up one unit
To shift a graph 5 units to the right, you do this to the (x) inside the parentheses
What is subtract 5?
True or False: Reflecting a graph changes its steepness
false
This term describes a transformation that actually changes the shape or "steepness" of the graph.
a non-rigid transformation
his is the equation for a parent function f(x) that has been reflected over the x-axis and moved 5 units right.
-f(x-5)
A translation is called this because the shape keeps its exact size and form.
rigid transformation
if the point is at (-3,4) and is reflected over the y axis. what is its new location.
(3,4)
in the equation y = frac{1}{4}x^2(, the graph will look this way compared to ) the graph will look this way compared to y = x^2$.
wider (or flatter)
Describe the two moves in f(x + 4) - 7.
left 4 and down 7