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Polynomial Functions
Rational Functions
Exponential Functions
Composed Functions
100

Using the points (0, 4), (1, 0), (2, 2), (3, 4), what type of polynomial best fits this data?

  • A) Linear
  • B) Quadratic
  • C) Cubic
  • D) Quartic

C) Cubic

100

Given f(x) = (x3 -4x2 -3x + 18)/(x2 + x - 6)

What is the horizontal asymptote of f(x)?

  • A) y = 0
  • B) y = 1
  • C) y = 3
  • D) No horizontal asymptote

C) y = 3

100

A data set models exponential decay and passes through the points (0, 20) and (3, 1.28). If the model is in the form f(x) = a(bx), what is the exact value of the decay factor b?

b = 0.4

100

Given g(x) = x2 and f(x) = x - 5, find the exact value of f(g(3)).

4

200

What is the y-intercept?

  • A) 0
  • B) 1
  • C) 5
  • D) -4

C) 5

200

Given f(x) = (x3 -4x2 -3x + 18)/(x2 + x - 6)

How many holes does this function have? If so, where is the hole?

1 hole; at x = 0

200

Perform the necessary manipulation to rewrite the function g(x) = 150(4x) into the equivalent form g(x) = 150(c2x) . What is the exact value of the new base, c?

c = 2

200

Given f(x) = x - 5 and g(x) = x2 write the simplified algebraic expression for g(f(x)).

(x-5)2

OR

x2 - 10x +25

300

Find the average rate of change of f(x) on the interval [0, 3]. Show your work.

Average rate of change = -3

300

Given f(x) = (x3 -4x2 -3x + 18)/(x2 + x - 6)

Is there a slant asymptote? If so what is the equation of the slant asymptote? 

Yes, Equation: y = x - 5

300

The value of a certain car model depreciates exponentially over time. The value of the car, V(t), in thousands of dollars, at various times t years after the car was purchased, is given below. The value can be modeled by the function: V(t) = abt

Time, t (years): 0 , 1 , 2

Value, V(t) (thousands): 30 , 24,  19.2


Use the given data to write two equations that can be used to find the values for constants a and b in the expression V(t).

(1) ab0 = 30

(2) ab1 = 24

300

Given h(x) = (√x+1), determine the domain of the composite function h(f(x)) in interval notation.

Note: f(x) = x-5 and x+1 is in the square root

[4, ∞)

400

Use cubic regression with the given points (-3, 176), (-2, 81) , (1.5, 0.5), (4, -27), (5,-80), (6,-175) to find the function. What is the equation?

f(x) = -2x³ + 9x² - 12x + 5

400

Find the coordinates of all x-intercepts (zeros) of f(x)

x = -2

400

Find the equation of the exponential function, f(x) = a(b)x , that exactly fits the data points in the table below. Express b as an exact simplified fraction.

Points: (-1, 12) , (1,3) 

f(x) = 6(1/2)x

400

Given g(x) = x2, find all real values of x such that g(3x) = 36.

x = plus or minus 2

500

Calculator Active. Given the table of values: Using the cubic regression find f(100) and find when f(x)=50.

{(-4, -85.7), (-3, -43), (-1, 3), (0, 10.2), (2, 10), (3, 8), (5, 17.5), (7, 62)}




 

Cubic Regression: 

f(x) = 0.525x3 - 3.14x2 + 4.19x + 10.16



f(100)=-1911195

Estimated: -1911

f(6.53619) = 50

Estimated: f(6.536) = 50

500

Which of the following describes all vertical asymptotes of f(x)?

A) x=2

B) x=-3

C) x=2 and x=-3

D) x=3 and x=-2

C) x=2 and x=-3

500

The area covered by a fungus doubles every day. The area covered on Day 4 is 160 cm2. Find the corresponding exponential function A(t) = abt that models the area, where t is the number of days. Then, find the initial area, A(0). 


A(t) = 10 (2)t; Initial Area A(0) = 10 cm2

500

Given f(x) = x - 5 and g(x) = x2, determine the domain of the composite function f(g(x)) in interval notation.

(∞,∞)