Function Fundamentals
For the school club's profit function T(x), what is a reasonable domain representing the number of tickets sold?
Whole Numbers
Is the expression 12-4x^3+x^5 in standard form?
No (the terms are not in descending order of exponents).
Solve the inequality 4x-5<15
x<5
Does the set of points {(1, 2), (2, 3), (3, 2), (4,5)} represent a function?
Yes, because every input has exactly one output.
Which expression represents how much longer a garden is with length (4x^2-x+5) and a width of (x^2+3x-2)?
3x^2-4x+7
Solve the following equation for x: 0.4(x+10)=0.1x+13.
x=30
Is the product of sqrt(3) and 7 rational or irrational?
Irrational (it cannot be expressed as a terminating or repeating decimal).
A projectile's height is modeled by h(t)=-5t^2+20t+2. What is its height at t=3 seconds?
17 meters
What is the completely factored form of the expression 3x^3-75x?
3x(x-5)(x+5)
Marcus has $4.50 in nickels and dimes, with 5 more dimes than nickels. Write an equation to find the number of nickels (n)?
.05n+.1(n+5)=4.5
Is the product of 2*sqrt(3) and sqrt(12) rational or irrational?
Rational (the product is 12)
Solve the compound inequality -4<2x-4<2 for x.
0<x<3
Could a relation with domain {0,2,4} and range {1,3,5} be represented by the ordered pairs {(0,1), (2, 5), (4,3)}?
Yes (it satisfies the definition of a function where each input has one output).
Simplify the following expression: (4 x^3 y^2)^2
16x^6 y^4
Compare the solutions of 5(x-2)=10 and 2x+8=4x. Are they equal or is one greater?
The solutions are equal (x=4)
Solve the volume of a pyramid formula V=1/3 lwh for the length l.
l=(3V)/(wh)
Sarah has 30. Notebooks cost $3.50 and pens cost $1.25. If she buys 4 notebooks, what is the max number of pens she can buy?
12 pens