name that parent function
The name of the graph of a rational function, f(x)=1/x.
Hyperbola
Sketch the graph of f(x) = x^2 - 5
A parabola that opens up, translated down 5 units.
a ___________ is a rigid transformation that has the affect of shifting the graph of a function up, down, left, or right
What is a Translation?
Quadratic function moved up 7 units
What is f(x) = x^2 + 7
f(x) = - (x + 7)
Reflected over x-axis and translated Left 7
Also acceptable: Reflected over x-axis and translated Up 7
Sketch a square root function that has been shifted left 4 and up 2.
y=sqrt(x+4) + 2
a __________ is a rigid transformation which produces a mirror image of the graph of a function with respect to a specific line.
What is a reflection?
Linear function moved left 18 units
What is f(x) = (x + 18)
The parent graph of this family has an endpoint on the origin (0, 0)
Sketch the graph of f(x)= - 1/(x-2) + 3
Hyperbola reflected over the x-axis, translated 2 units right and 3 units up.
When |a|>1 this results in this transformation
Vertical Stretch
Cubic moved left 2 units and down 35 units
f(x) = (x+2)^3 -35
The shape of this parent graph has a vertical asymptote at x=0 and a horizontal asymptote at y=0.
Hyperbola
Rational / Inverse / Reciprocal Function; f(x)=1/x
Sketch this absolute value function:
y= -0.5|x-3|+1
Opens down, vertex/maximum at (3, 1) and vertically compressed by a factor of 0.5 (fatter)
When 0<|a|<1 this results in this transformation.
A Vertical Compression
Quadratic moved right 53 and reflected across the x-axis
What is f(x) = -(x-53)^2 + 1
The parent function of this family of functions is V-shaped.
Absolute Value
Sketch the following cubic function:
f(x)= -(x+1)^3+3
Reflected over the x-axis, translated 1 unit left and 3 units up.
What do we call the "original" functions that are the root of all transformations?
Parent Function
cubic reflected across the y-axis, vertical stretch by 4, moved right 99, and up 11
What is f(x) = 4(-x-99)^3 +11