Parent Functions
Name the parent function and tell us what it would like like:
y = 3x + 4
Linear; straight line with positive slope
What is the domain of y = 2x - 1?
all Real numbers
Are f(x) = 2x - 2 and g(x) = 2x + 2 inverses?
No
How is this function transformed?
f(x) + 3
Vertically translated up 3 units
How can I tell when a relation is a function?
Graph: Vertical line test
Table/set of points: make sure each input is only used once
Name the parent function and tell us what it would like like:
g(x)= - x^2
Quadratic; parabola opening down (rainbow)
What is the inverse of g(x) = x - 1
g^-1 (x) = x + 1
How is this function transformed?
-f(x)
Reflected over the x-axis
Evaluate f(x) = 2x - 7 for x = -3
f(-3)= -13
Name the parent function and tell us what it would like like:
y = square root(x) - 4
Square root; opening to the right and up, from y-intercept of (0, -4)
What is the end behavior of x^2?
As x --> + infinity, y --> + infinity
As x --> - infinity, y --> + infinity
What is the inverse of f(x) = 3x - 1?
f^-1 (x) = (x+1)/3
How is this function transformed?
f(x-7)
Horizontally translated 7 units to the right
What is f(g(5)) when f(x) = 7x + 1 and g(x) = x^2 + x?
g(5) = 30 so f(g(5)) = f(30) = 211
Name the parent function and tell us what it would like like:
f(x) = (x+3)^3
Cubic; snakes up and to the right, passes through (-3, 0)
What is the domain of the square root of (x - 2)?
[2, infinity)
What is the inverse of {(3, 2), (-7, 1), (-1, 0)}?
{(2, 3), (1, -7), (0, -1)}
How is this function transformed?
(1/2)f(x)
Vertically compressed by a factor of 1/2
Draw a function that has a global maximum but NO global minimum.
Responses will vary.
Name the parent function and tell us what it would like like:
y = 0.5|x|
Absolute Value; looks like a V but in this case wider than the parent function (vertically compressed)
What are the range and end behavior of y = - |x+2| ?
(-inf, 0]
As x --> + infinity, y --> - infinity
As x --> - infinity, y --> - infinity
What is the inverse of the square root of (x-2)?
x^2 + 2
How is this function transformed?
f(-x)
Reflection over the y-axis
Find the average rate of change for y=x^3 on the interval -1 < x < 2
9/3 = 3