Rational vs Irrational
What is a the difference between a Rational and Irrational Number?
Rational- stops or repeats
Irrational- never stops, never repeats
What makes a relation a function?
One output for every input. (x don't repeat)
If f(x) = x + 6, find f(3).
9
In the function C(t), which variable represents the input.
t
A gym charges a $25 membership fee plus $10 per visit. Write a function for the total cost after x visits.
C(x) = 10x + 25
Rational or Irrational?
√49 + 92.50
Rational
Is {(1, 4), (2, 5), (3, 6)} a function?
yes
If g(x) = 4x − 3, find g(5)
17
If C(3) = 175, where C is cost and 3 represents hours, interpret the statement.
The cost for 3 hours is $175
A tank begins with 60 gallons and loses 4 gallons per minute. Write a function for the amount remaining after t minutes.
V(t) = 60 − 4t
Rational or Irrational?
The sum of a rational and irrational number.
irrational
What is the vertical line test?
A test that determines if a graph is a function by showing if any inputs (x) are repeating.
If h(x) = x² + 2x, find h(−3).
3
In P(n) = 12n + 30, where n is the number of shirts, this number represents the price per shirt.
12
A rental costs $80 for the first 2 hours and $30 for each additional hour. Find the cost for 5 hours.
$80 + $30(5 − 2) = $170
Rational or Irrational?
The product of a nonzero rational number and irrational number
irrational
A table has x-values −3, 0, 4, and 7 and y-values 2, 2, 5, and 5. Is it a function?
yes
If p(x) = −2x³ + 5, find p(2).
State the input and output.
p(2)=-11
input 2
output -11
In P(n) = 12n + 30, n represents the number of shirts, this number represents the initial design fee.
30
A student starts with $45, buys the same snack for 5 days, and has $32.50 left. Find the price of each snack.
$2.50
$45 − 5x = $32.50
Rational or Irrational?
The sum of a rational and irrational number.
Both rational and irrational
A student’s name is paired with every class the student takes during the school day. Does this relation represent a function if the student takes six different classes? Explain.
Not a function, because one input (the student’s name) is paired with more than one output (the six classes)
For p(x)=−2x+5, find p(x)=21.
State the input and output.
p(-8)=21
input -8
output 21
A rocket’s height is R(t) = −5t² + 25t + 3. Find and interpret R(2).
After 2 seconds, the rocket is 33 meters high
A movie theater charges $8 per ticket and can sell between 0 and 150 tickets. The function R(t)=8t represents the total ticket revenue. What is the range of this function in context?
0≤ y ≤1,200