Module A
Evaluate when a = -2 and b = 3
a2 / 2b
2/3
Is this a function? Why or why not
{(1, 2), (-1, 3), (2, 5), (1, 4)}
No because 1 goes to 2 and 4
What is the function found after the following operations are applied to f(x) = x2?
1) Reflect over x-axis
2) Left shift 2
3) Up shift 5
f(x) = -(x+2)2 + 5
Is this function increasing of decreasing? Why?
f(x) = 2(0.6)x
Decreasing because 0.6<1
What 3 domain restrictions do you have to look for (in this class)?
Fractions, square roots, logarithms
Simplify the expression
(3x5y3) / (6xy2)
(1/2)x4y
Solve the system of equations:
x-y= 5
-3x+3y = 2
No solution
Convert to vertex form:
f(x) = x2 - 6x + 4
f(x) = (x-3)2 - 5
What is the domain of f(x) = ln (5x-3)
(3/5, inf)
What is the inverse function of a logarithm?
Exponential
Solve for x:
x2 + 12x = -35
x = -5 and x = -7
If a drone descends by 20 feet every 2 seconds, what is the constant rate of change of its descent?
10 feet/second
What ticket price maximizes the number of visitors if the number of visitors V(p) is given by this function, where p is the ticket price
V(n) = -2n2 + 200n + 2500
$50
Solve for x:
sqrt(2) = 32x+2
x = -19/10
Name all of the MAT 117 academic staff
Katarina, Sarah, Bhavya, Parnika, Dushyant, Abraham
Fully factor the following expression:
6x2 - 13x - 5
(3x+1)(2x-5)
Find the inverse of f(x) = (x+6) / (2x + 3)
Find (f o g) (x) and find the domain.
f(x) = x2 + 1
g(x) = sqrt(x-1)
x
[1, inf)
Simplify ln( (x+1)2 / (x5(x+4)) )
2 ln (x+1) - 5 ln (x) - ln (x+4)
f(f^-1(x)) = x and f^-1(f(x)) = x
Simplify the rational expression:
(x+3) / (x+2) + x / (x-2)
Determine the domain of
sqrt(x+3) / (sqrt(x-1) - 4)
[1, 17) U (17, inf)
Find the vertical and horizontal asymptotes and holes of
f(x) = (x2 - 3x) / (x2 - 8x + 15)
VA: x=5
HA: y=1
Hole: (3, -3/2)
Solve for x:
log(x) + log(x+15) = 2
x=5
(1/27)2x+1=93x
x = -1/4