Parent Functions
What is a parent function?
A parent function is the most simple version of a equation.
What is the domain of the parent function y=√x?
x ≥ 0
Shifting the graph of y=x2 down 4 units results in this equation
y=x2-4
x+y=10
x−y=2
What is (6,4)?
Solve:
x+y+z=6
x+y−z=2
x−y+z=4
What is (3,1,2)?
What is the parent function for all quadratic equations?
y=x2
What is the range of the quadratic function y = -(x - 3)² + 5?
y ≤ 5
To shift the function y=|x| right 3 units you must replace x with this expression in the absolute value bars
x-3
Solve:
2x+y=7
x+y=5
What is (2,3)?
Solve:
x+y+z=9
x−y+z=5
x+y−z=7
What is (6,2,1)?
Write the equation for the parent function f(x)=x2 after its shifted 3 units right and 5 units up
g(x)=(x-3)2+5
What is the domain of the rational function y=4/x2-9
All real numbers except x = 3 and x = -3
This is the new vertex of the parabola y=(x+5)2+7 after it undergoes a horizontal shift left 5 and vertical shift up 7.
(-5,7)
How many solutions does this system have?
y=2x+3
y=2x−4
What is no solution?
Solve:
x+y+z=6
2x+y+z=8
x+2y+z=9
What is (2,3,1)?
If the parent function y=x2 shifted left 4 units and reflected over the x-axis and shifted up 3 units what is its final equation?
y= -(x+4)2+3
what is the range of the exponential function y=2x-1-4?
y > -4
If f(x)=x2, write the equation for shifting the graph left 4 units and down 3 units.
What is g(x)=(x+4)2−3?
Solve the system:
3x+2y=16
x−2y=0
What is (4,2)?
Solve:
2x+y−z=6
x−y+z=3
3x+y+z=10
What is (2,1,−1)?
y= 5x-7/x-2
What is the domain of the radical function y=√6-2x?
x ≤ 3
If f(x)=∣x∣, write the equation after reflecting over the x-axis, shifting right 2, and shifting up 5.
What is g(x)=−∣x−2∣+5?
Solve:
2x+3y=13
4x−3y=5
What is (3,73)?
Solve:
x+2y+z=8
2x−y+3z=9
3x+y−2z=4
What is (7/3,5/3,7/3)?