Equations
Solve 4x+5=21
What is 4
Solve 4x-3<2x+7
What is (5, infinity)
Find A+B
Problem #1
What is A+B=[{-2, 7},{6, 2}]
Find the domain, range, minimum, and maximum of the function if there are any
f(x)=-x^3+6x^2-9x-4
What is domain: (-infinity, infinity), range: (-infinity, infinity), minimum: (1,-8), and maximum: (3,-4)
Describe how the graph of the function, f(x)=(x-3)^2, can be obtained from its parent function
What is to shift the graph of y=x^2 right 3 units
Find the slope of the line containing the given points (1,4) and (-4,-2)
What is 6/5
Solve -4<=6-2x<4
What is (1, 5]
Find B-A
Problem #2
Find the intervals on which the function is increasing, decreasing, and/or constant
f(x)=8x/(x^2+1)
What is increasing: (-1,1) and decreasing: (-infinity, -1), (1,infinity)
Describe how the graph of the function, g(x)=-|x|+2, can be obtained from its parent function
What is to reflect y=|x| over x-axis and vertical shift up 2
Find the equation of the line containing the points (0,3) and (5,0)
What is y=(-3/5)x+3
2x+3<=-4 or 2x+3>=4
What is (-infinity, -7/2] U [1/2, infinity)
Find the product of A*B if possible
Problem#3
What is not defined
Find (fg)(x) given that f(x)=2x-1 and g(x)=-2x^2
What is (fg)(x)=-4x^3+2x^2
Write an equation for a function that has a graph with the given characteristics:
The shape of y=sqrt(x), but reflected across the y-axis and shifted left 2 units and down 1 unit
What is f(x)=sqrt(-(x+2))-1
City Cabs charges a $1.75 pickup fee and $1.50 per mile traveled. Diego's fare for a crosstown ride is $19.75. How far did he travel in the cab?
What is 12 miles
Jeanette can be paid in one of two ways for painting a house:
Plan A:$200 plus $12 per hour
Plan B:$25 per hour
Suppose that a job takes n hours to complete, for what values of n is plan A better Jeanette
What is n>15?
Find the product of A*B if possible
Problem#4
What is A*B=[{-10,28},{14,-26},{0,-6}]
Given that f(x)=5x-4, g(x)=x^3+1, and h(x)=x^2-2x+3, find each of the following
(fog)(1)
(goh)(2)
What is (fog)(1)=6 and (got)(2)=28
Write an equation for a function that has a graph with the given characteristics:
The shape of y=2^x, but reflected across the x-axis and shifted up 3 units
What is f(x)=-2^x+3
Richard is considering relocating to an assisted living facility. He learns that there is an initial community fee of $2250 and a monthly charge of $3380 for level-one care.
Write an equation that can be used to determine the total cost C(t) for t months of level-one care. Then find the total cost for 20 months.
What is C(t)=3380t+2250
What is C(20)=$69,850
Solve 4x(x-2)<2(2x-1)(x-3)
What is (-infinity, 1)
The produce manager at Stan's Market orders 40 lb of tomatoes, 20 lb of zucchini, and 30 lb of onions from a local farmer one week.
a)Write a 1x3 matrix A that represents the amount of each item ordered
b)The following week the produce manager increases his order by 10%, find a matrix B that represents this order
c)Find A+B and tell what the entries represent
What is
a) A=[40 20 30]
b) B=[44 22 33]
c) A+B=[84 42 63]; the total amount of each type of produce ordered for both weeks
Find f(x) and g(x) such that h(x)=(fog)(x)
h(x)=(x+2)^3-5(x+2)^2+3(x+2)-1
What is f(x)=x^3-5x^2+3x-1 and g(x)=x+2
Write an equation for a function that has a graph with the given characteristics:
The shape of y=x^2, but reflected across the x-axis and shifted right 3 units and up 4 units
What is f(x)=-(x-3)^2+4