Functions
Writing Functions
Key Features
Quadratic Forms
Polynomial Operations
100
Which relation is a function?
A. {(1,2), (1,3), (4,8),(8,4)}
B. {(2,5), (3,5),(6,5),(1,5)}
C. {(4,1), (4,1), (4,2),(3,5)}
D. {(1,2), (2,3), (2,4),(5,8)}
B
B. {(2,5), (3,5),(6,5),(1,5)}
100
Write a linear function with slope 3 and y-intercept 2.
y=3x+2
100
What is the y-intercept?
-4
100
Which form is y=ax2+bx+c?
Standard Form
100
Simplify:
(2x+3)+(x+5)
3x+8
200
What is f(3) if f(x)=2x+5?
11
200
A quantity triples every hour starting at 8.
Write AND identify the function type.
y=8(3)x, exponential
200
What are the roots of the graph?
No real roots
200
What are the zeros of (x−3)(x+2)?
x=3, -2
200
(5x−2)−(2x+3)
3x-5
300
A table shows:
x: 1, 2, 3, 4
y: 2, 6, 18, 54
Which type of function best models the data? Justify.
Exponential
300
A population grows by 20% each year starting at 50
y=50(1.2)x
300
A graph increases, then decreases.
What feature must it have?
Maximum (turning point)
300
Which form is BEST for finding zeros quickly? Why?
Factored form (set each factor = 0)
300
(3x2+2x)−(x2−4x)
2x2+6x
400
Which situation represents an exponential function?
A. changes by a difference of 5 each month
B. changes by a linear rate of 4
C. increases by adding 11 each day
D. increases by a factor of 3 each year
D. increases by a factor of 3 each year
400
Table:
x: 1, 2, 3
y: 2, 5, 8
Write the function.
y=3x-1
400
A quadratic has x-intercepts at −2 and 4.
What is its axis of symmetry?
x = 1
400
Convert y=(x−1)(x−5) to standard form.
y=x2−6x+5
400
(x+2)(x2−x+1)
x3+x2−1x+2
500
A graph that is symmetrical and made of straight lines
What is absolute value?
500
A company charges a $25 fee plus $10 per hour.
Another charges $15 per hour only.
Write both functions AND determine when they cost the same.
y=10x+25, y=15x
Solve: x = 5
500
Function: y=−2(x−3)2+5
Identify:
- Vertex
- Max/Min
- Direction of opening
Vertex: (3, 5)
Max
Opens down
500
Two functions:
y=(x−2)2+1
y=(x−2)2−3
How do their graphs compare?
Second is shifted down 4 units → lower minimum
500
A student expands:
(x+3)2=x2+9
Explain the mistake and give correct answer.
Missing middle term
Correct: x2+6x+9