Linear Equations and Inequalities
3n - 5 = -8(6 + 5n)
-1
Is the below relationship a function? (Consider the vertical line test.)
A = {(0,2) (3, 5) (4, 5)}
Yes
5x + y = 9
10x - 7y = -18
(1, 4)
Describe the transformation of the function below from its base function
f(x) = -0.5(x +1)2-3
reflect over the x-axis, compress by a factor of -1/2, left one, down three
(2y)/3 + y/2 = 7
y = 6
Describe the domain and range of the function below:
B = {(2, 4), (5, 8), (-1, 3)}
Domain = -1, 2, 5
Range = 3, 4, 8
Solve the system.
-3x + 7y = -16
-9x + 5y = 16
(-4, -4)
Find the inverse of the function
f(x) = -2x +5
(x - 5)/-2 = y
-6 < 14 - 5x < 12
(2/5, 4) or 2/5 < x < 4
Given f(x) = 5x2 - 3 and g(x) = (4x - 1)/2x +3
Find f(4) + g(-1)
72
Solve the system.
y = 6x - 11
-2x - 3y = -7
(2, 1)
Find the inverse of the function
g(x) = (5x - 2)/(x + 7)
g-1(x) = (-7x - 2)/(x - 5)
|5x -3| =7
x = 2, -4/5
Given f(x) = 5x2 - 3 and g(x) = (4x - 1)/2x +3
find g(f(0))
*don't worry if you get a fraction!
13/3
The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.
Van: 8, Bus: 22
Describe what the vertical and horizontal line tests tell you about a function and its inverse.
The vertical line test tells you if a relation is a function; the horizontal line test tells you if the relation's inverse is a function.
|4x + 12| < 10
-5.5<x<-0.5
Find the domain for each function:
g(x) = (5x +1)/3x - 4
f(x) = the square root of 4x + 36
x cannot equal 4/3
x is greater than or equal to -9
Solve the system.
x + y + z = 2
6x - 4y + 5z = 31
5x + 2y + 2z = 13
(3, -2, 1)
Find the inverse of g(x) = 4 - 5x
g-1(x) = (x - 4)/-5