Introduction to Parent Graphs & Transformations #1

Parent Graphs & Transformations #1

Parent Graph

A parent graph is the simplest graph for a family of functions.

Families of Graphs

You should be able to identify which family a graph belongs to by shape or equation.

The linear parent

y = x

The linear parent passes through

(0, 0) and has a slope of 1.

Multiple Choice

Which graph belongs to the linear family?

Multiple Choice

Which graph belongs to the linear family?

Linear Equations

All linear equations will have the form y = mx + b

Multiple Choice

Which equation is a linear equation?

•  $y=x^2+1$  

•  $y=\left|x\right|-2$  

•  $y=2x+3$  

•  $y=2\sqrt{x}$  

Multiple Choice

Which equation is a linear equation?

•  $y=\frac{1}{2}x-4$  

•  $y=\ ^3\sqrt{x-2}$  

•  $y=x^3+2$  

•  $y=\sqrt{7x}$  

The Quadratic Parent  $y=x^2$  

Quadratic graphs are a U shape. The parent graph passes through 

(0, 0), then (1, 1), and (2, 4).

Multiple Choice

Which graph belongs to the quadratic family?

Multiple Choice

Which graph belongs to the quadratic family?

Quadratic Equations

Quadratic equations will have an

 $x^2$  in the equation. 

Multiple Choice

Which equation is a quadratic equation?

•  $y=x^2+1$  

•  $y=\left|x\right|-2$  

•  $y=2x+3$  

•  $y=2\sqrt{x}$  

Multiple Choice

Which equation is a quadratic equation?

•  $y=\frac{1}{2}x-4$  

•  $y=\ ^3\sqrt{x-2}$  

•  $y=x^3+2$  

•  $y=5x^2+6$  

The Cubic Parent $y=x^3$  

Also called the cube parent. This graph passes through (-1, -1), (0, 0), and (1, 1). Then it curves upward and downward.

Multiple Choice

Which graph is a cubic graph?

Multiple Choice

Which graph is a cubic graph?

Cubic Equations

Cubic equations (or cube) will have an

 $x^3$  in the equation.

Multiple Choice

Which equation is a cubic equation?

•  $y=x^2+1$  

•  $y=\left|x\right|-2$  

•  $y=4x^3-1$  

•  $y=2\sqrt{x}$  

Multiple Choice

Which equation is a cubic equation?

•  $y=\frac{1}{2}x-4$  

•  $y=\ ^3\sqrt{x-2}$  

•  $y=x^3+2$  

•  $y=5x^2+6$  

Absolute Value Parent y = |x|

The graph is a V shape and passes through (0, 0), (-1, 1) and (1, 1).

Multiple Choice

Which graph belongs to the absolute value family?

Multiple Choice

Which graph belongs to the absolute value family?

Absolute Value Equations

The equations will always have x between vertical bars | x |

Multiple Choice

Which equation is an absolute value equation?

•  $y=x^2+1$  

•  $y=\left|x\right|-2$  

•  $y=4x^3-1$  

•  $y=2\sqrt{x}$  

Multiple Choice

Which equation is an absolute value equation?

•  $y=\frac{1}{2}x-4$  

•  $y=\ ^3\sqrt{x-2}$  

•  $y=x^3+2$  

•  $y=\left|5x+6\right|$  

Transformations

• Shift- when the graph moves up, down, left, or right

• Reflection- when the graph is "flipped" over the x or y-axis.

• Vertical stretch or compression- the graph will look "skinnier" or "fatter"

Multiple Choice

What transformation has occurred to the parent graph? The dashed graph is the parent.

• The graph shifted down 4 units.

• The graph shifted right 4 units.

• The graph shifted up 4 units.

• The graph shifted left 4 units.

Multiple Choice

What transformation has occurred to the parent graph? The dashed graph is the parent.

• The graph shifted down 1 unit.

• The graph shifted right 1 unit.

• The graph shifted up 1 unit.

• The graph shifted left 1 unit.

Multiple Choice

What transformation has occurred to the parent graph? The dashed graph is the parent.

• The graph shifted down 1 unit.

• The graph reflected over the x-axis.

• The graph reflected over the y-axis.

Multiple Choice

What transformation has occurred to the parent graph? The green dashed graph is the parent and the blue solid graph is the transformed graph.

• The graph shifted down 1 unit.

• The graph reflected over the x-axis.

• The graph reflected over the y-axis.