Building Functions - Common Core Standards

High School Algebra Practice


This quiz illustrates the range of difficulty expected by the following Common Core State (CCS) standards:

QuestionCommon Core Standard #
indicates a modeling standard.

All questions of this quiz illustrate the difficulty of the high school F.BF standards required for all students, including the college and career ready students.

Questions 1: A train travels at a speed of 50 miles/hour and then starts decelerating at time t0. The decrease in speed is linear with time, and for each hour travelled the speed decreases 2 miles/hour.
The time travelled from time t0 until the train stops is hours.

Question 2: A bacterial colony doubles its size every 24 hours. Write an equation that describes the number of bacteria in the colony at the end of the nth day, S(n), in terms of the number of bacteria in the colony at the end of day (n-4), S(n-4).

Question 3: Given


which of the following functions is h(x)=f(g(x))?

Questions 4 and 5:


Given the sequence of table above, the formula for the n-th term is:

The 55th term of the sequence above is:

Questions 6 and 7:

x ≠ -4

The solution of the equation f(x) = 0.5 is x =

Which of the following is the inverse function of f(x)?

Question 8: Consider the following four functions:

f(x) = x2 - 4, x > -1
g(x) = x2 - 4, x < -1
h(x) = 4 - x2, x < 1
i(x) = 4 - x2, x > -1

Function has an inverse function.

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