Transformations of Functions

The video tutorial explains transformations of functions, focusing on vertical stretches, horizontal shifts, and reflections. It uses a general function f(x) to illustrate how multiplying by a constant affects the graph. The tutorial also covers the importance of absolute values in determining whether a transformation is a stretch or compression and highlights the difference between inside and outside transformations. Finally, it simplifies transformations by factoring and clarifies common misconceptions.

What happens to a function when it is multiplied by 2 on the outside?

• It reflects over the x-axis.

• It undergoes a vertical stretch.

• It compresses vertically.

• It shifts 2 units to the right.

What is the transformation when a function is multiplied by 2?

• Horizontal stretch

• Horizontal compression

• Vertical stretch

• Vertical compression

What is the effect of subtracting 3 inside the function?

• The graph shifts 3 units to the right.

• The graph shifts 3 units to the left.

• The graph stretches vertically.

• The graph compresses horizontally.

What is the effect of subtracting a number inside the function?

• The graph shifts up.

• The graph shifts down.

• The graph shifts right.

• The graph shifts left.

What does multiplying a function by a negative number on the outside do?

• It compresses the graph horizontally.

• It shifts the graph up.

• It reflects the graph over the x-axis.

• It reflects the graph over the y-axis.

What is the transformation when a function is multiplied by 3/2?

• Vertical stretch

• Vertical compression

• Horizontal compression

• Horizontal stretch

What is the effect of a negative sign inside the function?

• Shifts the graph down

• Reflects over the x-axis

• Reflects over the y-axis

• Shifts the graph up

What is the result of multiplying by a negative number inside the function?

• Shifts the graph down

• Reflects over the x-axis

• Reflects over the y-axis

• Shifts the graph up

What is the transformation when a function is multiplied by a negative number on the outside?

• Reflects over the y-axis

• Shifts the graph down

• Reflects over the x-axis

• Shifts the graph up

What is the result of multiplying by a number greater than 1?

• Horizontal stretch

• Vertical stretch

• Horizontal compression

• Vertical compression