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.
When reflecting across the x-axis, the negative sign is placed in front of the entire function. This changes the sign of every output value, flipping the graph from above the x-axis to below it.
Conditions: The reflection is across the x-axis.; The negative sign applies to the whole function value.
When reflecting across the x-axis, the negative sign is placed in front of the entire function. This changes the sign of every output value, flipping the graph from above the x-axis to below it.
Conditions: The reflection is across the x-axis.; The negative sign applies to the whole function value.
Reflection across the y-axis is written algebraically by placing a negative sign only on the input variable x inside the function argument. This changes the sign of the input, mirroring the graph horizontally.
Conditions: The reflection is across the y-axis.; The negative sign is applied only to the input variable x.
Reflection across the y-axis is written algebraically by placing a negative sign only on the input variable x inside the function argument. This changes the sign of the input, mirroring the graph horizontally.
Conditions: The reflection is across the y-axis.; The negative sign is applied only to the input variable x.