Transformations of Parent Functions Explained

The video tutorial covers parent functions and their transformations. It begins with an introduction to various parent functions such as constant, linear, quadratic, cubic, square root, reciprocal, absolute value, and step functions. The tutorial then explains how to transform these functions through translations, reflections, and stretches/compressions, using both examples and function notation. The lesson includes practical examples of graphing transformed functions and analyzing their changes. The session concludes with an assignment involving IXL practice and a worksheet.

Which of the following is the correct representation of a constant function?

• f(x) = 1/x

• f(x) = x^2

• f(x) = c

• f(x) = x

What is the basic shape of the quadratic parent function?

• A hyperbola

• A straight line

• A step function

• A parabola

How do you move a function to the left by 2 units?

• Subtract 2 from the function

• Add 2 to the function

• Replace x with x + 2

• Replace x with x - 2

What happens to a function when you add a positive constant outside the function?

• It moves up

• It moves to the left

• It moves to the right

• It moves down

How do you vertically stretch a function by a factor of 2?

• Add 2 to the function

• Multiply the function by 2

• Subtract 2 from the function

• Multiply the function by 1/2

What is the effect of placing a fraction between 0 and 1 in front of a function?

• Horizontal stretch

• Vertical compression

• Vertical stretch

• Horizontal compression

How do you reflect a function over the y-axis?

• Place a negative sign inside with x

• Place a negative sign outside the function

• Add a negative constant to the function

• Subtract a negative constant from the function

What is the result of reflecting a function over the x-axis?

• The function is flipped vertically

• The function remains unchanged

• The function is shifted up

• The function is flipped horizontally

If g(x) = 0.5|x| + 4, what transformations have been applied to the parent function f(x) = |x|?

• Vertical stretch and move right

• Vertical compression and move left

• Vertical compression and move up

• Vertical stretch and move down

For the function g(x) = 2x^2 - 4, what transformations have been applied to the parent function f(x) = x^2?

• Vertical compression and move up

• Vertical stretch and move down

• Vertical compression and move down

• Vertical stretch and move up