Parent Functions
What is a parent function???
A parent function is the most basic, unmodified equation of a specific function family.
What is the domain of f(x)=x?
All real numbers
What transformation happens to f(x)=x2 to create g(x)=x2+6?
Up 6 units
Solve: x+y=10, x=4
x=4, y=6
what is the solution to x+y=6 and x=2?
(2,4)
What is the vertex of (f(x) = x^2)
(0,0)
What is the domain of f(x)=x2?
All real numbers
What transformation happens to f(x)=x2 to create g(x)=(x−3)2?
Right 3 units
Solve: x+y=8, x−y=2
x=5, y=3
What is the solution to y=2x+1 and y=5?
(2,5)
f(x)=x What is the equation of the parent linear function?
f(x)=x
What does the range of a function represent?
All possible output values (y-values)
What transformation happens to f(x)=x2 to create g(x)=(x+2)2?
Left 2 units
Solve: 2x+y=9, x+y=5
x=4, y=1
What is the solution to y=x+3 and y=2x+1?
(2,5)
What is the y-intercept of f(x)=x?
0
What is the range of f(x)=x2?
y≥0
In f(x+4), which direction does the graph move?
Left 4 units
Solve: 3x+y=11, x−y=1
x=3, y=2
How many solutions do two lines have if they intersect at exactly one point?
One Solution
On a piece of paper, solve
𝒇 𝒙 = 𝒙𝟒 − 𝟐 𝐆𝐫𝐚𝐩𝐡 𝒉 𝒙 = 𝒙𝟒 − �
𝒉 𝒙 = 𝟏 𝒙 − 𝟐 + 𝟒 𝒉 𝒙 = 𝟏 𝒙B𝟐 + 𝟒 Parent function 𝒇 𝒙 = 𝟏 𝒙 Transformation: Translated 4 units up Translated 2 units right 𝑫 = −∞, 𝟐) ∪ (𝟐, ∞ 𝑹 = −∞, 𝟒) ∪ (𝟒, ∞
What is the domain of f(x)=1x?
x≠0
In f(x−2), which direction does the graph move?
Right 2 units
Solve: 2x+3y=13, x+y=5
x=2, y=3
How many solutions does a system have when the two equations represent the same line?
Infinitely many solutions