EQUATIONS
LINES
FUNCTIONS
INVERSE FUNCTIONS
EXPONENTIAL & LOGARITHMIC FUNCTIONS
100
Solve for x: 4x + 12 = -3 - 2x
x = -5/2
or
x = -2.5
100
What are the intercepts of the line y = 1/8x - 3?
x-intercept: (24,0)
y-intercept: (0,-3)
100
What is the domain of the following function: f(x) = sqrt(3 - 5x)
Domain: (-oo, 3/5]
100
If f(120) = 25. What is the value of f -1(25)?
f -1(25) = 120
100
4x+6 = 4-2x-2
x = -8/3
200
3/4x + 6 = 4/5x
x = 120
200
Find the slope of the line below
m = -1/2
200
What is the domain of the following function: f(x) = (2x - 5)/(-2 - 7x)
Domain: (-oo, -2/7) U (-2/7, oo)
200
Given a graph, how do you sketch its inverse?
You swap the x and y values of the points.
200
3x = 10
x = log(10)/log(3)
300
x2 - 100 = 0
x = 10
or
x = -10
300
Find the slope of the line that passes through the points (7,17) and (10,8)
m = -3
300
On which intervals is the function increasing and decreasing?
Increasing: (-oo, -3) U (3, oo)
Decreasing: (-3,3)
300
Find the inverse of the following function:
f(x) = 3x - 2
f-1(x) = (x + 2)/3
300
7(2x - 3) = 49
x = 5/2
or
x = 2.5
400
x2 = -25
x = 5i
or
x = -5i
400
What is the equation of the line parallel to y = -2x + 4 with y-intercept at (0,-9).
y = -2x - 9
400
What is the local maxima/minima of the graph?
Local maxima: y = 50
Local minima: y = -50
400
Find the inverse of the following function:
f(x) = (4x + 3)/(1 - x)
f-1(x) = (x - 3)/(4 - x)
400
log2(4x) = 5
x = 8
500
6x2 + 7x = 3
x = 1/3
or
x = -3/2
500
What is the equation of the line perpendicular to y = 6x - 1 with y-intercept at (0,21).
y = -1/6 x + 21
500
Given the original function f(x) = x. What transformations are performed to get to the function f(x) = (x - 1)/4 - 5?
1. Shifted to the right 1 unit
2. Stretched horizontally by a factor of 4
3. Shifted down 5 units
500
If the inverse of a function is f -1(x) = sqrt(3x - 5). What is the original function f(x)?
f(x) = (x2 + 5) /3
500
log(3x - 10) = log(4 + x)
x = 7