Identify The Parent Function
Identify the parent function of y = 3(x - 4) + 7
Identify the parent function of y = 3(x - 4) + 7
For y = |x - 3| + 2, state the vertex.
(3, 2)
Describe the transformation from y = |x| to y = |x - 3| + 2
Shift right 3 and up 2.
Solve |x + 8| = 6.
x = -2 or x = -14.
What is the point where an absolute value graph changes direction called?
The vertex
Identify the parent function of y = -2(x - 3)^2 + 5.
Quadratic: y = x^2
For y = 3|x - 1|, state the domain
All real numbers.
Describe the transformation from y = |x| to y = -|x + 3| + 1.
Reflect across the x-axis, shift left
3, and up 1.
Solve |5x - 8| = 0.
x = 8/5.
What does an x-intercept represent on a graph?
A point where y = 0 and the graph
crosses or touches the x-axis.
Identify the parent function of y = -4|x + 2| + 1.
Absolute value: y = |x|
For y = -|x + 3| + 1, does the graph open up or down?
Down.
If p(x) is h(x) shifted up 2 units, write p(x) in terms of h(x).
p(x) = h(x) + 2.
Solve |2x - 10| = 12
x = 11 or x = -1.
What does it mean for a function to be increasing on an interval?
As x increases, the function's
y-values increase.
Identify the parent function of y = 2sqrt(x - 5) - 3.
Square root: y = sqrt(x)
For y = |x - 5| - 2, state the x-intercepts.
x = 3 and x = 7, so (3,0) and (7,0)
If n(x) is m(x) shifted right 7 units, write n(x) in terms of m(x)
n(x) = m(x - 7).
Solve 4|x + 10| - 4 = 8.
x = -7 or x = -13.
What does the domain of a function describe?
The allowable/input x-values
Identify the parent function of y = 3(2)^(x + 1) - 4.
Exponential: y = b^x
DAILY DOUBLE: For f(x) = -2|x + 2| - 1, give the vertex, range, and end behavior
Vertex (-2,-1); range y <= -1; as x ->
+/- infinity, f(x) -> -infinity.
A graph changes from y = |x| to y = 3|x - 1|. Describe every transformation.
Shift right 1 and vertically stretch
by a factor of 3.
DAILY DOUBLE: Solve |5x - 28| + 7 = 20.
x = 3 or x = 41/5
In a real-world model, why might the domain need to be restricted even if the parent function has all real numbers as its domain?
The context may make some x-values impossible or meaningless, such as negative time or negative mileage.