Functions (Algebraic)
Functions (Numerical)
Functions (Visual)
Functions (Verbal)
Random
100
If f(x) = x2 + x + 1, then what is f(3)?
f(3) = 32 + 3 + 1 = 13
100
The above table gives the world population P at a given year t. What is P(1950)?
2,560,000,000 people
100
What is g(0)?
g(0) = -2
100
The rule that the US Postal Service used as of 2019 is as follows: the cost is 1 dollar for up to 1 oz, plus 15 cents for each additional ounce (or less) up to 13 oz.
What is the cost of sending a letter that weighs 3 oz?
$1.30
100
What is the area of a triangle? Let b = base and h = height.
A = (b*h)/2
200
What is f(x) is the following piecewise function, what is f(1.5)?
f(x) = {(x,if 0\leq x \leq 1),(2-x, if 1 < x \leq 2),(0, if x >2):}
1.5 < 2 so f(1.5) = 2 - 1.5 = 0.5
200
Does the following table represent a function? Why or why not? 
No. A function is a rule that assigns to each input element x exactly one output element y. In the table, the input x = 5 has two different output elements y = 7 and y = 8, so this table does not represent a function.
200
What is g(2)?
g(2) = 1
200
A storage container has a total volume of 125 cm3. If we know that the storage container is in the shape of a cube, what are the dimensions of the container?
5 cm x 5 cm x 5 cm = 125 cm3
200
What is the equation of a line? Describe each variable.
y = mx + b, where m = slope of line, b = y-intercept (called slope-intercept form)
OR
y - y1 = m(x - x1), where m = slope of line, (x1,y1) is any point on the line (called point-slope form)
300
If f(x) = x3 - x and g(u) = u3 - u, is it true that f = g?
Yes, two functions are equal to one another if and only if they agree (that is, they are equal) for every input.
300
Give an algebraic expression to describe the function of the table below. 
y = 2x + 1
300
Estimate what g(2.1) is.
g(2.1) is a little less than 3 (perhaps ~ 2.9)
300
A rectangular box has a total volume of 10 in3. The length of its base is twice its width. Let l = length of base, w = width of base, and h = height of box. Give an expression for the height of the box in terms of either l or w.
h = 10/(2w^2)in = 5/w^2 in or h = 20/l^2 in
300
Completely expand the following algebraic expression:
(2x + 1)(3x - 4)(x + 1)
6x^3+x^2-9x-4
400
If f(x) and g(x) are the following functions, is it true that f = g?
f(x) = (x^2-x)/(x-1) and g(x) = x
No. For f to be equal to g, we must have f(x) = g(x) for all inputs of x. Consider when x = 1. Then we have that g(1) = 1, however f(1) is undefined (that is, it does not exist).
f(1) = (1^2-1)/(1-1) = 0/0
400
The table below gives the tuition cost y of a school for a given year x. Does the table describe y as a function of x? Why or why not? 
Yes, each year has exactly one tuition cost, so y is indeed a function of x.
400
For what values of x is f(x) greater than or equal to g(x)? 
-2 \leq x \leq 2
400
An open-topped cylinder has a radius of 2 ft and a height of 5 ft. What is the total surface area of the open-topped cylinder?
24 \pi ft^2
400
If f(x) and g(x) are the following functions, what is f(g(x))?
f(x) = 1/3\sqrt{x^2 + 2x-1} + 4x and g(x) = x^2+3
f(g(x)) = 1/3 sqrt(x^4+8x^2+14)
500
If f(x) and g(x) are the following functions, what is f(g(4))?
f(x) = \sqrt(4x+1)/(3x^2) and g(x) = x+2
x=5/108
500
500
State the solution of the equation f(x) = -1. 
The equation f(x) = -1 does not have a solution (in other words, there is no value of x such that f(x) = -1).
500
A rectangular box with an open top has a total volume of 10 m3. The length of its base is twice its width. Material for the base costs $10 per square meter; material for the sides cost $6 per square meter. Express the cost of materials as a function of the width of the base.
C(w) = 20w^2 + 180/w, \text{ for } w > 0
500
If f(x), g(x), and h(x) are the following functions, then find f(g(h(x))).
f(x) = |x^2-4|, g(x) = 2^x, h(x) = sqrt{x} + 1
f(g(h(x))) = |2^{2\sqrt{x}+2}-4|