Parent Function
Equation of
Function Name of function Sketch of Graph Special Features / Symmetry Domain Range
• straight line that goes through
the origin
• slope is 1
Linear
𝑓 (𝑥) = 𝑥 Function • divides the plane exactly in Χ∈R 𝑌∈𝑅
half diagonally
• graph in 1 and 3 quadrant
• parabola opening up
• vertex at the origin
𝑓 (𝑥 ) = 𝑥 2 Quadratic • 𝑦 has the minimum value
Function Χ∈R 𝑦≥0
• 𝑦 − 𝑎𝑥𝑖𝑠 = axis of symmetry
(vertical line that divides the
parabola into two congruent
halves.)
• graph in 1 and 2 quadrant
1
Equation of
Function Name of function Sketch of Graph Special Features / Symmetry Domain Range
• straight line that goes through
the origin
• slope is 1
Linear
𝑓 (𝑥) = 𝑥 Function • divides the plane exactly in Χ∈R 𝑌∈𝑅
half diagonally
• graph in 1 and 3 quadrant
• parabola opening up
• vertex at the origin
𝑓 (𝑥 ) = 𝑥 2 Quadratic • 𝑦 has the minimum value
Function Χ∈R 𝑦≥0
• 𝑦 − 𝑎𝑥𝑖𝑠 = axis of symmetry
(vertical line that divides the
parabola into two congruent
halves.)
• graph in 1 and 2 quadrant
1
