Functions and Gaphing
State the vertex:
f(x)=(x−4)^2+1
(4,1)
Solve:
4x−5=11
x=4
What is the degree of:
x^3-2x+1
3
What is the y-intercept of a graph?
Where the graph crosses the y-axis
OR
The point where x=0
What is Mr. Castro's favorite fruit?
Mango/Strawberry
You cut a pizza into 8 slices and eat 3. What fraction is left?
5/8
If
f(x)=2x^2−1
find:
f(3)
17
Solve:
x^2−9=0
x=±3
x^2−16
(x−4)(x+4)
What are the zeros of a function?
The x-values where the graph equals zero
OR
The x-intercepts
What is Mr. Castro's favorite sport(s)
soccer
volleyball
golf
A party has 7 rows of 6 chairs on one side and 5 rows of 6 chairs on the other side. How many chairs total?
72
Describe the transformations:
y=−2(x−3)^2+5
Solve the system:
y=2x+1
y=−x+10
(3,7)
Factor completely:
x^2+7x+12
(x+3)(x+4)
What are the zeros of a function?
The x-values where the graph equals zero
OR
The x-intercepts
This is Mr. Castro’s favorite fast food restaurant.
in-n-out / McDonalds
You have $45. You spend $17 and then $7. How much money do you have left?
$21
Find: f(x) * g(x)
if
f(x)=x+3
and
g(x)=2x−1
2x^2+5x-3
Solve:
sqrt{x+1}=5
x=24
Use synthetic division:
(x^3 −4x+1)÷(x−2)
Answer:
x^2+2x
remainder:
1
State the difference between domain and range.
Domain → all possible x-values
Range → all possible y-values
This is the combination of three things Mr. Castro believes creates the best classroom learning environment.
collaboration
risk taking
precistance
A movie ticket costs $8 for students and $12 for adults. A group buys 15 tickets and spends $144 total.
How many student tickets and adult tickets were purchased?
student = 9
adult = 6
Given:
f(x)={(x,+,2,,x<1),(x^2,,,,x>=1):}
Find: f(−3) and f(2)
f(−3)=−1
f(2)=4
Solve:
x^2+4x+20=0
x=−2±4i
A polynomial has zeros:
−1, 2, 5
Write a possible polynomial.
(x+1)(x−2)(x−5)
Describe the end behavior of:
f(x)=x^3
As x→−∞, f(x)→−∞
As x→∞, f(x)→∞
What year was Mr Castro born in?
1995
A cafeteria sells tacos and burritos.
Tacos cost $3 and burritos cost $5.
A student buys 10 items and spends $42.
How many of each did they buy?
tacos=4,
burritos=6