Unit 1
A polynomial function p is given by p(x) = -x(x - 4)(x + 2). What are all intervals on which p(x) is greater or equal to 0?
(-infinite, -2] and [0,4]
True or False: If f(x) = x3, then f is an odd function.
True
True or False: The degree of a polynomial is the highest exponent of any term in the expression.
True
What is the hole for the function, f(x) = (x - 2)(x + 2)/ (x - 2) (x - 3) ?
2
x = 4
What is the domain of the function f(x) = square root of x + 2?
[-2, infinite)
True or False: A function can have more than one output for a single input.
False
Find the horizontal asymptote of f(x) = 2x2 + 5/ x2 - 1
2
The function π is defined by f(x) = asin(b(x + c)) + d, for constants a, b, c, and d. In the xy-plane, the points (2,2) and (4,4) represent a minimum value and a maximum value, respectively, on the graph of f. What are the values of a and d ?
a = 1 and d = 3
The rate of people entering a subway car on a particular day is modeled by the function π , where π (t)=0.03t3 - 0.846t2 + 6.587t + 1.428 for 0β€ t β€20. π (t) is measured in people per hour, and t is measured in hours since the subway began service for the day. Based on the model, at what value of t does the rate of people entering the subway car change from increasing to decreasing?
t = 5.505
The functions f and g are given by f(x) = log(x - 1) + log (x + 3) and g(x)= log(x + 9). In the xy-plane, what are all x-coordinates of the points of intersection of the graphs of f and g?
x = 3 only
Describe the transformation of the function k(x) = -(x + 2)2 + 4
Reflection over the x-axis, shift 2 units to the left and shift 4 units up
What creates a hole in a function?
Common factors in the numerator and denominator cancel out.
Let π be a rational function that is graphed in the xy-plane. Consider x = 1 and x = 7. The polynomial in the numerator of π has a zero at x = 1 and does not have a zero at x = 7. The polynomial in the denominator of π has zeros at both x = 1 and x = 7. The multiplicities of the zeros at x = 1 in the numerator and in the denominator are equal. What are the holes and/or vertical asymptote, if any, does graph f has?
A hole at x = 1 and a vertical asymptote at x = 7
The polynomial function p is given by p(x) = (x + 3)(x2 - 2x - 15). How many distinct real zeros does p have?
Two distinct real zeros
The function f is given by f(x) = sin2.25x + 0.2. The function g is given by g(x) = f(x) +0.5. What are the zeros of g on the interval 0β€ x β€π ?
1.540 and 2.471
What is true about each input of all functions?
They have exactly one output
If a function increases but its rate is decreasing, what does that say about its concavity?
Its concave down
What is the vertical asymptote for the function h(x) = (x - 2) (x + 3)/ (x - 3) (x - 2)
x = 3
In a certain simulation, the population of a bacteria colony can be modeled using a geometric sequence, where the first day of the simulation is day 1. The population on day 4 was 4,000 bacteria, and the population on day 8 was 49,000 bacteria. What was the population of the colony on day 6 based on the simulation?
14,000
If f(x) = 2x + 1 and g(x) = x2, find f(g(x)).
2x2 + 1
What are all values of π, for 0 β€ π <2π, where 2sin2π = -sinπ ?
0, π , 7π/6 , 11π/6
Describe the end behavior of f(x) = -3x4 + 2x2 - 1
As x increases, f(x) decreases
As x decreases, f(x) decreases
Find all real zeros of the function, f(x) = (x - 4)(x + 1) (x - 1)
x = 4,-1, and 1
Simplify log(1000)
3