Composition
If f(x) = 2x + 3 and g(x) = x², find (f ∘ g)(2)
11
f(x) = x + 2 if x < 0;
3x if x ≥ 0
. What is f(–1)?
1
If f(x) = 4x – 5, find f(3).
7
What are graphs with a straight line called
Linear
What is the domain of a function?
The x values
If f(x) = x – 4 and g(x) = 2x, find (g ∘ f)(5)
2
f(x) = { 2x if x ≤ 1; x² if x > 1 }. Find f(2)
4
If g(x) = 3x², find g(–2).
12
What are graphs with a U-shaped called
Quadratic
What is the range of a function?
All possible y-values
If f(x) = x² + 1 and g(x) = √x, find (f ∘ g)(9)
10
Given f(x) = { x + 1 if x < 0; 2 if x ≥ 0 }. Find f(0)
2
If p(x) = 2x – 7, find p(5)
3
What are graphs with a V-shaped called
Absolute value
Define the intercepts of a graph
Where the function (line) crosses an axis
If f(x) = x + 2 and g(x) = 1/x, find (g ∘ f)(3).
1/5
: Graph f(x) = { –x if x < 0; x if x ≥ 0 }. What does it look like? (What is the shape?)
V-shape (absolute value)
If k(x) = 2x³ – x, find k(–1)
-1
What are graphs with multiple parts called
Piecewise functions
The line that cuts a quadratic graph into two equal parts
Axis of symmetry
If f(x) = 2x and g(x) = x² – 1, find (f ∘ g)(–3)
16
f(x) = { x² if x < 2; 4x – 3 if x ≥ 2 }. Find f(2).
5
If m(x) = √(x – 1), find m(10).
3
Its graph starts at a point (the endpoint) and curves slowly upward.
The function increases as x increases, but at a decreasing rate (flattens out
Square root function
f(x) = -3(x+4)2-5
Describe the transformation
(there are four parts to the answer)
Reflect over the x-axis,
Stretch vertically by 3,
Shift left 4 units,
Shift down 5 units.