To translate the graph of y=f(x) four units left and three units down, replace x with x+4 inside the function argument and subtract 3 outside the function. The final transformed equation is y=f(x+4)−3.
Conditions: The starting graph has equation y=f(x).; The intended transformation is a horizontal translation 4 units left and a vertical translation 3 units down.
To translate the graph of y=f(x) four units left and three units down, replace x with x+4 inside the function argument and subtract 3 outside the function. The final transformed equation is y=f(x+4)−3.
Conditions: The starting graph has equation y=f(x).; The intended transformation is a horizontal translation 4 units left and a vertical translation 3 units down.
A parent function is the simplest representative form of a family of functions. In this clip, the quadratic parent function is illustrated by y=f(x)=x2, whose basic graph is a parabola.
Conditions: Used as the starting function before transformations are applied.; The example shown is quadratic, but the spoken definition is general.
A parent function is the simplest representative form of a family of functions. In this clip, the quadratic parent function is illustrated by y=f(x)=x2, whose basic graph is a parabola.
Conditions: Used as the starting function before transformations are applied.; The example shown is quadratic, but the spoken definition is general.
The clip introduces transformations as operations applied to a parent function’s graph. The named categories are translations (shifts left, right, up, down), reflections (across the x- or y-axis), and vertical stretches or compressions.
Conditions: These are presented as general ways to modify the graph of a parent function.; Only horizontal and vertical translations and reflections are actually solved within this clip.
The clip introduces transformations as operations applied to a parent function’s graph. The named categories are translations (shifts left, right, up, down), reflections (across the x- or y-axis), and vertical stretches or compressions.
Conditions: These are presented as general ways to modify the graph of a parent function.; Only horizontal and vertical translations and reflections are actually solved within this clip.
Moving left uses plus inside the function argument because horizontal translations modify the input variable. To shift the graph left by h units, you must replace x with x+h so that the function evaluates the original input at a point h units to the right, effectively moving the graph left.
Conditions: The transformation is a horizontal translation of the graph of y=f(x).; The shift amount is a positive constant.
Moving left uses plus inside the function argument because horizontal translations modify the input variable. To shift the graph left by h units, you must replace x with x+h so that the function evaluates the original input at a point h units to the right, effectively moving the graph left.
Conditions: The transformation is a horizontal translation of the graph of y=f(x).; The shift amount is a positive constant.