1) Select all of the following tables which represent y as a function of x and are one-to-one.
a.
b.
c.
2) For the following function, evaluate: f(-2),f(-1),f(0),f(1),and f(2).
f(x)= 3x/2x
3) Find the domain of the following function.
f(x)= √((x+5))/(x-3)
4) Find the average rate of change of the below function over the interval of x values specified.
f(x)=4x2 - 7 on [-1, 2]
5) For the function graphed below, estimate the locations of the local extrema, inflection point(s), and the intervals over which the function is increasing, decreasing, concave up, and concave down.
6) For the pair of functions below, find the composite functions f(g(x))and g(f(x)). Simplify your answers if possible.
f(x)= 1/(x2+2) and g(x)=4x+3
7) Write an equation for the transformed toolkit function graphed below.
8) For the function below, find the inverse function f-1 (x).
f(x)=-3x+2
9) Find the equation of a linear function with x-intercept at point (-5, 0) and y-intercept at point (0, 4).
10) Find the point of intersection (if any) of the following two functions.
f(x) = x + 5 and g(x) = 2x - 2
11) Find the equation of a line perpendicular to the line defined by the function below and passing through the point (4, 2).
f(x) = 2x+4
12) A hypothetical student is working on a 25-question take-home final exam. After 1 hour, the student has completed 4 questions. After 3 hours, the student has completed 12 questions. Assuming a linear rate of completion, how long will it take the student to complete the exam?
13) Solve the following equation.
|4x + 2| = 15
14) Find the vertical and horizontal intercepts of the function below.
g(x) = x2 + 2x - 4
15) Rewrite the quadratic function below in vertex form.
f(x) = 2x2 - x - 3
16) Write a formula for the polynomial graphed below.
17) For the function below, find the horizontal intercept(s), the vertical intercept(s), the vertical asymptote(s), and the horizontal asymptote(s).
f(x)= (2x2-3x-20)/(x2-5)
18) Find a formula for an exponential function passing through the points (1, 2) and (3, 6).
19) A population is growing at a continuous rate of 3% per year. If the population is 125,000 today, what will the population be 5 years from now?
20) Solve the following equation for x.
log x = 5
21) Solve the equation for the variable.
10e-0.03t = 4
22) A radioactive substance decays at a continuous exponential rate. Starting from 200 mg, after 26 hours, 132 mg remains. How much of the substance will remain after 40 hours?
23) If $1000 is invested in an account earning 2% compounded quarterly, how long will it take the account to grow in value to $1500?
24) Solve for the variable x in the following equation.
log (x+5) - log x+1) = 2
25) Find the time required for an investment to double in value if invested in an account paying 3% compounded monthly.