Exploring the Transformation of Functions

The video tutorial reviews the transformation of parent functions, including constant, linear, quadratic, absolute value, cubic, and square root functions. It explains different types of transformations such as vertical and horizontal translations, reflections, and dilations. The tutorial provides examples to illustrate these transformations, helping students understand how to identify parent functions and describe transformations applied to them.

Which of the following is the equation for a constant function?

• f(x) = a number

• f(x) = x^2

• f(x) = |x|

• f(x) = x

What is the effect of adding a number to the entire function?

• Reflects the function over the x-axis

• Compresses the function vertically

• Shifts the function up

• Shifts the function to the left

How do you shift a function to the right by b units?

• Divide the function by b

• Multiply the function by b

• Subtract b from the x values

• Add b to the x values

What happens when you make the entire function negative?

• Reflects over the y-axis

• Shifts down

• Reflects over the x-axis

• Shifts up

If a function is multiplied by a number between 0 and 1, what transformation occurs?

• Vertical stretch

• Horizontal compression

• Vertical compression

• Horizontal stretch

Identify the parent function and transformation: f(x) = (x - 1)^2

• Linear function, shift left 1 unit

• Quadratic function, shift right 1 unit

• Absolute value function, shift left 1 unit

• Cubic function, shift right 1 unit

What is the transformation for f(x) = x^3 - 5?

• Shift up 5 units

• Shift down 5 units

• Shift left 5 units

• Shift right 5 units

Write the equation for a cubic function reflected over the x-axis and translated 9 units down.

• -x^3 + 9

• x^3 - 9

• -x^3 - 9

• -f(x) - 9

What is the transformation for f(x) = |x + 4| - 1?

• Shift left 4 units, up 1 unit

• Shift right 4 units, up 1 unit

• Shift left 4 units, down 1 unit

• Shift right 4 units, down 1 unit

For the function y = 2(x - 3)^2 - 2, what transformations have been applied?

• Vertical compression by 2, shift right 3 units, shift up 2 units

• Vertical stretch by 2, shift left 3 units, shift down 2 units

• Vertical compression by 2, shift left 3 units, shift up 2 units

• Vertical stretch by 2, shift right 3 units, shift down 2 units