Rewrite as an exponential equation.
log2 1/32= -5
(Hint: base of 2)
What is 2^-5 = 1/32
100
Use substitution to solve the system.
x=2y-8
4x+5y=33
What is y=5, x=2
100
Find f(g(x)) and g(f(x)). Then, determine whether f and g are inverses of each other.
f(x)=(x+7)/2
g(x)=2x+7
What is f(g(x))=x+7, g(f(x))=x+14: f and g are not inverses
100
The one-to-one functions g and h are defined as follows. Then, find the following.
g(x)={(-2,5), (3,9), (6,-7), (9,-3)}
h(x)=4x-13
a) g^-1(9)
b) h^-1(x)
c) (h^-1oh)(1)
What is 3, y=(x+13)/4, 1
200
Use the properties of logarithms to expand
log(zx^6)
What is logz+6logx
200
Compute the following and round you answer to 3 decimal places.
log5(8)
(Hint: base is 5)
What is 1.292.
200
Solve the following system of equations.
2x+4y=-8
-2x+3y=22
What is y=2, x=-8
200
Given: h(x)=7x/(x-4) Find the following.
a) h-1(x)
b) Domain (h-1)
c) Range (h-1)
What is y= -4x/(7-x), (-infinity, 7)U(7, infinity), (-infinity, 4)U(4, infinity)
200
Find the x-intercept(s) and the coordinates of the vertex for the parabola
y= x^2+8x+7
What is vertex (-4,9), x=-7,-1
300
Write the expression as a single logarithm.
(1/5)log2x+3log2y-log2z
(Hint: base is 2)
What is log2([x^(1/5)y^3]/z)
300
Solve for x.
log4(x-4)=1-log4(x-7)
(Hint: base is 4)
What is x=8
300
Solve the following system of equations.
x+2y=8
-x-2y=8
What is no solution.
300
Find all x-intercept(s) and y-intercept(s).
f(x)=-x^3-2x^2+8x
What is y=0, x=0, x=-4,x=2
300
Determine the end behavior.
a) f(x)=3x^5-4x^3+4x^2+7
b) f(x)=-2x^4+4x^3-6x^2+3x
c) f(x)=-5x(2x-5)^2
What is falls left rises right, falls left and right, rises left fall right.
400
Solve for x.
9^(-x-2)=27
What is x=-7/2
400
Solve for x and round your answer to the nearest hundredth. e^(x+5)=15
What is x=-2.291
400
Solve the following system of equations.
-x-2y=-2
x+2y=2
What is infinitely many solutions: y=(-x/2)+1
400
Determine the end behavior and the zeros will touch or cross on the graph.
a. f(x)=-3(x+1)2(x+3)2
What is falls on right and left, zeros: -1(touches), -3(touches)
400
Determine the end behavior and the zeros will touch or cross on the graph.
a. h(x)= x^3-x^2-6x
What is falls on left rises on right, Zeros:0,3,-2 (all cross)