Domain & Range
Find the domain of the following function.
f(x) = 3x5 + 16x3 + 27x - 15
(-infinity, infinity)
Find (f(g(x)) where
f(x) = 1/x
g(x) = x2+5
1/(x^2+5)
Identify the parent function and list all transformations.
f(x) = -(x-1)2 + 11
DOUBLE JEOPARDY!!
Parent Function: f(x) = x^2
Reflection across the x-axis
Horizontal Shift Right 1
Vertical Shift Up 11
Determine if the following function is even, odd, or neither.
f(x) = -5x2 + 4
Even
Find the slope of the line containing the points (0, 3) and (-4, 5)
-1/2
Find the domain of the following function.
f(x) = sqrt(3-x)
(-infinity, 3]
Find g(f(x)) where
f(x) = sqrt(x-5)
g(x) = x2 + 5x -7
DOUBLE JEOPARDY!!
x + 5sqrt(x-5) - 12
Identify the parent function and list all transformations.
f(x) = 2/(x+1) - 5
Parent Function: f(x) = 1/x
Vertical Stretch by 2
Horizontal Shift Left 1
Vertical Shift Down 5
Determine if the following function is even, odd, or neither.
f(x) = 16x3 - 3x/4
Odd
Find the equation of the line containing the points (0,5) and (-1, -3).
y = 8x + 5
Find the domain of the following function.
f(x) = 3/sqrt(x-5)
(5, infinity)
Determine if the following functions are inverses of each other
f(x) = 3/(2x-1)
g(x) = (3+x)/2x
Yes
5|x - 4| - 7 = 2
x = 11/5, x = 29/5
Use the piecewise function to evaluate f(-3) where
f(x) is defined by:
x^3 if x < -1
-2 if -1 < x < 4
sqrt(x) if x > 4
-27
Find the equation of a line parallel to the line y = 3x + 5 that passes through the point (2,-1)
y = 3x-7
Find the domain of the following function.
f(x) = (x+3)/(x^2-25)
(-infinity, -5) U (-5, 5) U (5, infinity)
Find the inverse function.
f(x) = sqrt(7x+15)
f-1(x) = (x2-15)/7
|3x - 4| < 8
(-4/3, 4)
Use the piecewise function to evaluate f(4) where f(x) is defined by
2x - 3 if x < 0
-3x^2 if x > 2
-48
A bakery charges $3.50 per cupcake in addition to a one-time service fee of $1.50. Write an equation for the function C(x) that describes the cost of purchasing x cupcakes. How much does it cost to buy a dozen cupcakes?
C(x) = 3.50x + 1.50
C(12) = $43.50
f(x) = sqrt(x+3)/(x^2-7x+10)
[-3, 2) U (2, 5) U (5, infinity)
Find the inverse function.
f(x) = 5x2 - 1
f-1(x) = sqrt[(x+1)/5]
|3x - 5| > 13
(-infinity, -8/3) U (6, infinity)
Determine if the following function is even, odd, or neither
f(x) = (2x+1)/(x+3)
Neither
A town’s population has been growing linearly. In 2003, the population was 45,000, and the population has been growing by 1,700 people each year. Write an equation, P(t), for the population t years after 2003. What was the population in 2007?
P(t) = 1,700t + 45,000
P(4) = 51,800