Transformations of Square Root Functions

The video tutorial explains how to graph a square root function using translation methods. It begins by identifying the basic graph of the square root of x. The tutorial then demonstrates horizontal and vertical translations, shifting the graph left by one unit and up by two units, respectively. The final section provides a rough sketch of the translated function, summarizing the process of graphing using translations.

What is the first step in graphing a square root function using translation?

• Identify the basic graph

• Reflect the graph

• Perform a vertical shift

• Rotate the graph

What does the basic graph of the square root of x look like?

• A curve starting at the origin

• A straight line

• A circle

• A parabola

What is the general form of a square root function?

• f(x) = x^3

• f(x) = √x

• f(x) = x^2

• f(x) = 1/x

In the order of transformations, which can be done first?

• Rotation

• Reflection

• Horizontal shift

• Vertical shift

What does adding 1 inside the square root function do to the graph?

• Shifts it up by one unit

• Shifts it down by one unit

• Shifts it left by one unit

• Shifts it right by one unit

What is the effect of a horizontal shift on the x-values of the graph?

• Increases all x-values

• Divides all x-values

• Decreases all x-values

• Multiplies all x-values

What is the effect of adding 2 outside the square root function?

• Shifts the graph down by two units

• Shifts the graph left by two units

• Shifts the graph right by two units

• Shifts the graph up by two units

What is the result of adding a constant outside the square root function?

• Reflection

• Horizontal shift

• Rotation

• Vertical shift

What is the effect of a vertical shift on the y-values of the graph?

• Multiplies all y-values

• Decreases all y-values

• Increases all y-values

• Divides all y-values

What is the purpose of graphing the basic square root function first?

• To calculate the area under the curve

• To find the y-intercept

• To use it as a guide for transformations

• To determine the slope