Function Family Album

Linear Family: Marc, Linda, Bobby, and Kimberly

Blue - Mark

Mark's equation is the dad of this family. He is considered the parent function since his equation is y = x.

Purple - Linda

Linda, Mark's wife, is the reflection of Mark, or the parent function, meaning that all of her points are Mark's points reflected over the x-axis.

Black - Bobby

Bobby, their first child, is a compression of the parent function, meaning that Mark's points were multiplied by a certain number, 1/2, resulting in Bobby's points.

Green - Kimberly

Their second child, Kimberly, is a vertical translation of the parent function, meaning that all of her points are Mark's points shifted either up or down. In this case, they were shifted up 2 spaces

Domain of parent function: All Real numbers

Range: All Real numbers

X-intercept: (0,0) Y-intercept: (0,0)

Max: ∞ Min: -∞ End Behavior: down,up

Intervals of increase: when the x is both negative and positive, the y also increases and goes up

Quadratic Family: Jon, Sue, Luke, Mary, Kenny

Blue: Jon

Jon is the dad, or parent function of the quadratics family. He has a standard equation of y = x^2

Purple: Sue

Sue is Jon's wife, and she is the reflection of him. She is a reflection of Joe over the x-axis, meaning that all of Jon's y-values multiplied by negative 1 results in her points.

Red: Luke

Luke, their first son, is a horizontal translation of Jon, as him and all of his points moved 2 spaces left, compared to Jon's points

Green: Mary

Mary, their only daughter, is a vertical translation of the parent function. Compared to the parent function, all of her points were shifted up by 3

Black: Kenny

Kenny, their third child, is a vertical stretch of Jon, his parent, causing him to slim down. All of his y-values were multiplied by 2 after being squared.

Domain of parent function: All Real numbers

Range: y ≥ 0

X-intercept: (0,0) Y-intercept: (0,0)

Max: ∞ Min: 0 End Behavior: up, up

Intervals of increase: When the x is both positive and negative the y value goes up to the value of x^2.

Cubic Family: George, Olivia, Ava, Aaron, Mia

Blue: George

George is the parent or parent function of the cubic family. His equation is y = x^3

Purple: Olivia

Olivia, George's wife, is a reflection of George over the x-axis. This means that all of George's y-values were multiplied by -1 in order to find Olivia's y-values

Green: Ava

Ava, their first child, is a vertical translation of the parent function. This means that her points were all shifted either up or down a certain number of spaces. In this case, her points were moved down 1 space.

Black: Aaron

Aaron, their first son, is a vertical compression of the parent function, George. This means that all of Aaron's points were multipled by a number in between 0 and 1, causing him to widen.

Red: Mia

Mia, their third child, is a horizontal translation of the parent function. This means that all of her points were shifted left or right a certain number of spaces. In this case, her points were moved right 2 spaces.

Domain of parent function: All Real numbers

Range: All Real numbers

X-intercept: (0,0) Y-intercept: (0,0)

Max: ∞ Min: -∞ End Behavior: down, up

Intervals of increase: when the x is positive the y goes up to x^3, and when the x is negative the y goes down to x^3

Absolute Value Family: Will, Anna, Chloe, Zoe, Joey

Blue: Will

Will is the parent of the Absolute Value family/. His equation is y =|x|

Black: Anna

Anna, Will's wife, is the reflection of the parent function over the x-axis. This means that all of Will's y-values are multiplied by -1 in order to find Anna's y-values.

Purple: Chloe

Chloe, their first child, is a horizontal translation of the parent function. This means all of her points were shifted left or right a certain number of spaces. In this case, her points were shifted right 5 spaces

Green: Zoe

Zoe, their second child, is a vertical translation of the parent function, This means all of her points were shifted up or down a certain number of spaces. In this case, her points were shifted left 5 spaces

Red: Joey

Joey, their third child, is a compression of Will, the parent function. All of his points were multiplied by a certain number, in this case 1/3.

Domain of parent function: All Real numbers

Range: y ≥ 0

X-intercept: (0,0) Y-intercept: (0,0)

Max: ∞ Min: 0 End Behavior: up, up

Intervals of increase: When the x is both positive and negative, the y value goes up to the absolute value of x.

Square Root Family: Josh, Emily, Nick, Leo, Theo

Blue: Josh

Josh is the dad of the family. He is considered the parent function since his equation is y = √x

Black: Emily

Emily, the wife, is a reflection of Josh. This means that she is negative and her line is reflected on the x-axis.

Green: Nick

Nick, their son, is a down translation of Josh. This means that all of Nick's points were moved down a certain number of spaces, in this case, 5.

Red: Leo

Leo, their second son, is a stretch of the parent function. All of his points were multiplied by a certain number, in this case 3.

Purple: Theo

Theo, their third son, is a left translation of Josh. This means all of Theo's points were moved to the left a certain amount of spaces, and in this case the number of spaces was 3.

Domain of parent function: x ≥ 0

Range: y ≥ 0

X-intercept: (0,0) Y-intercept: (0,0)

Max: ∞ Min: 0 End Behavior: up

Intervals of increase: When the x is positive, the y increases to the square root of the

Cubic Root Family: Juan, Maria, Jose, Mateo, Sofia

Blue: Juan

Juan is the parent of this family. His equation is y = x^1/3

Black: Maria

Maria, Juan's wife, is a reflection of Juan over the x-axis, meaning that all of Maria's y-values are Juan's multiplied by -1

Red: Jose

Jose, their first child, is a vertical stretch of the parent function, y=x^1/3. This means all of Jose's points are multiplied by a certain number, in this case 3, after being cubed.

Green: Mateo

Mateo, their second child, is a vertical translation of the parent function. This means that all of his points were shifted up or down a certain number of spaces. In this case, his points were moved up 4 spaces.

Purple: Sofia

Sofia, their first daughter, is a horizontal translation of Juan. This means all of her points were shifted left or right a certain number of spaces. In this case, her points were shifted left 5 spaces.

Domain of parent function: All Real numbers

Range: All Real numbers

X-intercept: (0,0) Y-intercept: (0,0)

Max: ∞ Min: 0 End Behavior: up, up

Intervals of increase: When x is positive, the y-value goes up to the cube root of x, and when x is negative, the y-value goes down to the cube root of x.