Linear Functions and Systems
A gym charges an initial membership fee and separate monthly membership fee. The function modeling the total fee for x months of membership is
f(x) = 30x+25
What does the number 30 represent?
The monthly membership fee
What are the 3 methods of solving a system of equations?
Graphing, Substitution, Elimination
Rewrite 165/2 as a radical expression
Square root of 165
What is the vertex of f(x) = x2+2x-3?
(-1, -4)
Write a function for the pattern:
3, 6, 12, 24, 48...
HINT: y = abn-1
y = 3(2)n-1
f(x) = 15x+120
Solve the system:
y+2 = 3(x-1)
y = -2x+10
(3,4)
Simplify (2x+8)(5x-7)
10x^2 +26x - 56
What are the x-intercepts of f(x) = x2+2x-3?
HINT: first factor into two sets of parenthesis, then set each parenthesis equal to 0
-3 and 1
The rabbit population on an island is 150 and doubles every year.
Write an equation to represent this growth.
HINT: y = abx
y = 150(2)x
Create an ordered pair that is a solution to the equation:
5y - 2x = 5
Pick any number for x, then solve for y!
330 children (c) and adults (a) attended a play.
There were 21 times as many children as adults.
This can be modeled by the system:
c = 21a
a+c = 330
How many children attended the play?
315 children
Simplify (2x2+3)(x+4)
2x^3 + 8x^2 + 3x +12
Find one solution to the system:
y = x^2 - 9
y = -2x - 1
HINT: Use substitution, then factor, then plug one answer back in!
(2, -5) or (-4, 7)
The current bat population is 27,000 and grows at an annual rate of 2%. Write an equation representing the bat population after x yrs.
HINT: y = abx
y = 27,000(1.029)x
The second term in a sequence is 5 and the fourth term is 12. Find the first term, f(1)
1.5
What 2 numbers have a sum of 217 and a difference of 85?
66 and 151
Simplify (2x-3) + [4x(3x+2)]
12x^2 +10x-3
Solve 16x^2 + 10x - 27 = -6x + 5
HINT: Get = to 0, then either factor or use quadratic formula!
1 or -2
The first 4 terms of a sequence are:
27, 32, 37, 42
Find the 60th term
Linear Regression:
Which correlation coefficient represents weak correlation? -.982, .204, or 1
.204
Simplify (3x2)2 - (y)2
9x^4 - y^2
Find the solutions to the system
y = 3x - 2
y = x^2
HINT: Use substitution, then factor, then plug both answers back in!
(1, 1) and (2, 4)