Exploring Transformations of Parent Functions

This video tutorial covers chapter one, section five on parent functions and transformations. It begins with an introduction to basic parent functions such as linear, absolute value, quadratic, and cubic functions. The tutorial then explains transformations, including horizontal and vertical shifts, stretches, and shrinks. Graphing examples are provided to illustrate these transformations, with a focus on square root and cubic functions. Advanced graphing techniques are discussed, including the use of Desmos for visualizing transformations. The video concludes with a reminder to practice graphing and seek additional help if needed.

What is the shape of the graph for a linear function?

• A horizontal line

• A straight line with a slope of 1

• A U-shape

• A V-shape

Which parent function has a V-shape?

• y = √x

• y = 1/x

• y = |x|

• y = x^2

What does a minus sign in front of 'h' indicate in a transformation?

• Shift up

• Shift to the right

• Shift to the left

• Shift down

If a function is vertically stretched, what happens to its graph?

• It shifts down

• It gets wider

• It shifts up

• It gets narrower

What is the effect of a negative sign in front of a function?

• Shift to the left

• Flip over the y-axis

• Shift to the right

• Flip over the x-axis

In the transformation of a square root function, what does a '+4' indicate?

• Shift to the left 4 units

• Shift to the right 4 units

• Shift down 4 units

• Shift up 4 units

What is the parent function of a cubic function?

• y = x^2

• y = x^3

• y = √x

• y = |x|

What does a vertical shrink by a factor of 1/3 do to a graph?

• Makes it wider

• Makes it narrower

• Shifts it up

• Shifts it down

How does a vertical stretch by a factor of 2 affect a parabola?

• Shifts it down

• Makes it narrower

• Shifts it up

• Makes it wider

What tool is recommended for graphing transformations?

• Excel

• Calculator

• Graph paper

• Desmos