For the questions below, enter your answers using interval notation. You can use "U" to represent a "union", e.g. enter "(1,2) U (3,5)" for (1,2)∪(3,5). You can enter "oo" for ∞, e.g. enter "(-oo, oo)" for (−∞,∞).
Suppose f(x) = 2x^2 + 4. What is the domain of f?
What is the range of f?
Suppose g(x) = √(x-5)/(x-11). What is the domain of g?
What is the range of g?
A 51-gallon tank is filled with water, and then water begins draining from the tank at a constant rate of 2 gallons per minute. The function f(t) = 51 - 2t determines the number of gallons of water in the tank, v, given the number of hours t since the water began draining. What is the range of f?
0 ≤ t ≤ 51
0 ≤ f(t) ≤ 25.50
0 ≤ t ≤ 25.5
0 ≤ f(t) ≤ 51
All real numbers
Suppose f(x) = (x-3)^2 and g(x) = √(x+7). Evaluate the following expressions.
f(g(3)) =
g(f(-12)) =
Which of the following represents all values of x whose distance from 7 is less than 8? Select all that apply.
|x-8| < 7
|x-8| > 7
|x-7| ≤ 8
|x-7| < 8
Which of the following represents all values of r whose distance from 0.8 is more than 4? Select all that apply.
|r-0.8| < 4
|r-0.8| > 4
|r-4| < 0.8
|r-4| > 0.8
Which of the following represents all values of s whose distance from -3 is no more than 3? Select all that apply.
|s-3| < 3
|s+3| < 3
|s-3| ≤ 3
|s+3| ≤ 3
A car is driving away from a stop sign. The formula d = t^2 + 3t expresses the car's distance from the stop sign in feet, d, in terms of the number of seconds, t, since the car started moving. Determine the car's average speed over the interval of time from t = 2 seconds to t = 5 seconds.
40 feet per second
30 feet per second
3 feet per second
18 feet per second
10 feet per second
The table contains some input-output pairs for the functions f and g.
x f(x) g(x)
3 4 6
4 10 3
6 6 7
7 7 7
10 3 4
Evaluate the following expressions.
f(g(6)) =
f^(-1)(6) =
g^(-1)(6) =
f^(-1)(g(6)) =
Suppose f(x) = (x-3)^2 and g(x) = √(x+7). Evaluate the following expressions.
f(g(3)) =
g(f(-12)) =