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.
The expression −f(x−5) represents a reflection across the x-axis combined with a horizontal shift 5 units right, because the negative sign is outside the function. The expression f(−x−5) represents a reflection across the y-axis combined with a horizontal shift 5 units right, because the negative sign is only on the input variable x inside the function.
Conditions: The base function is y=f(x).; Both expressions include a horizontal shift 5 units right.
The expression −f(x−5) represents a reflection across the x-axis combined with a horizontal shift 5 units right, because the negative sign is outside the function. The expression f(−x−5) represents a reflection across the y-axis combined with a horizontal shift 5 units right, because the negative sign is only on the input variable x inside the function.
Conditions: The base function is y=f(x).; Both expressions include a horizontal shift 5 units right.