Domain & Range
Find the domain of the following function.
π(π₯)=9/(π₯β6)
(-infinity, 6) U (6, infinity)
Find f(g(x)) given
f(x) = |x|
g(x) = 5x + 1
f(g(x)) = |5x + 1|
Identify the parent function & all transformations
f(x) = -(x-1)2 + 2
Parent Function: f(x) = x^2
Reflect across the x-axis
Horizontal Shift Right 1
Vertical Shift Up 2 units
Determine if the following function is even, odd, or neither.
f(x) = -5x2 + 4
DOUBLE JEOPARDY!!
Even
Find the slope of the line containing the points (-1, 3) and (2, 5)
2/3
Find the domain of the following function.
f(x) = sqrt(1+x)
DOUBLE JEOPARDY!!
[-1, infinity)
Find g(f(x)) given
g(x) = sqrt(x) + 2
f(x) = x^2 + 3g(f(x)) = sqrt(x^2 + 3) + 2
Identify the parent function and all transformations.
f(x) = 3/(x+4) - 5
Parent Function: f(x) = 1/x
Vertical Stretch by 3
Horizontal Shift Left 4 units
Vertical Shift Down 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 the line containing the points (1,5) and (-1, -3).
y = 4x +1
Find the domain of the following function
f(x) = (3x+1)/(4x+2)
(-infinity, -1/2) U (-1/2, infinity)
Identify if the following functions are inverses of each other
f(x) = x/(x+2)
g(x) = -2x / (x-1)
Yes
(DOUBLE JEOPARDY!!)
5|x - 4| - 7 = 2
x = 11/5, x = 29/5
Determine if the following function is even, odd, or neither.
f(x) = -3x5+ x3 -10x
Odd
Find the equation of a line perpendicular to the line y = x/2 + 5 that passes through the point (2, 1)
y = -2x + 5
Find the domain of the following function.
f(x) = (x+3)/sqrt(x-7)
(7, infinity)
Find the inverse of the following function.
f(x) = sqrt(5x-8)
f^-1 (x) = (x^2 + 8 )/ 5
|3x - 4| < 8
-4/3 < x < 4
(-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
At noon, a barista notices that they have $20 in their tip jar. If the barista makes an average of $0.50 from each customer, how much will they have in the tip jar if they serve π more customers during the shift? 7 more customers?
20 + 0.50n
$23.50
Find the domain of the following function.
f(x) = sqrt(x+5) / (x-3)
[-5, 3) U (3, infinity)
Find the inverse of the following function
f(x) = (2x+3)/(5x+4)
f^-1 (x) = (3-4x) / (5x-2)
|3x - 5| > 13
x < -8/3 , x > 6
(-infinity, -8/3) U (6, infinity)
Determine if the following function is even, odd, or neither
f(x) = (2x+1)/(x+3)
Neither
A townβs 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