Reverse! Inverse!
For the one-to-one function f(x)=2x+3, find the equation of the inverse.
f-1(x)=x/2-3/2
Suppose f(x)=-5|x|. Give one of the two transformations from the parent graph g(x)=|x| to the graph of f(x).
1. Flipped over the x-axis.
2. Stretched vertically by a factor of 5.
Expand the logarithmic function log2 2x3.
log22+3log2x=1+3log2x
VERTEX
Let f(x)=-(x2)+1 and g(x)=2x-2. Find f(1)-g(-2).
f(1)-g(-2)=6
For the one-to-one function f(x)=x/3-3, find the equation of the inverse.
f-1(x)=3x+9
Suppose f(x)=(x+3)2+4. Give two of the two transformations from the parent graph g(x)=x2 to the graph of f(x).
1. Horizontal shift: 3 units to the left.
2. Vertical shift: 4 units up.
Write (or say) the single logarithm function of log2(x+2)-1/2log2y.
log2(x+2)/y^1/2
This is a logarithm with a base of 10.
COMMON LOGARITHM
The larger of two numbers is 4 more than twice the smaller. If the smaller is subtracted from the larger, the result is 7. Write the system of two variables (x and y) which will find the two unknown numbers.
y=2x+4 and y-x=7
If a function f(x) is one-to-one, then an inverse function of f(x) exists. TRUE/FALSE?
TRUE!
Graph the line f(x)=1/2 * x and label 2 points. Hold it up so I may check on it!
Answers may vary, but the line goes through the origin and has a slope of 1/2. Two example points: (0,0), (2,1)
Solve log3x=-2.
1/9
The ________________ expression y=logb x is equivalent to the expression x=by.
LOGARITHMIC
Let the system be y-1/2 * x=2 and 2y-x=3. Find the solution set.
Empty set. The terms cancel and the resulting statement is false.
Using the graph of f(x)=x2+2, for x>=0, define two ordered pairs of f-1(x). I will graph f(x) on the front board for you!
(2,0), (6, 2), (11, 3)
Graph the function f(x)=-2x. Label 2 points on the graph of f(x)
Answers may vary, but as x tends to neg. infinity, f(x) tends to 0 and as x tends to infinity, f(x) tends to infinity. Example points: (0,-1), (1, -2)
Solve log39=x-1.
x=3
Two linear equations that have infinitely many solutions in common is said to be _________________ equations.
DEPENDENT
Find the vertex of f(x)=x2-2x+1
(1, 0)
Is the function f(x)=-(x2)for x>= 0 one-to-one? Give one or two points that demonstrate this.
The y-coordinate is the same and the x-coordinate is different. ie. (1,-1) and (-1,-1).
Graph the perpendicular line to the line y=3x-1, which goes through the point (0,6).
Answer must be a line of slope -1/3 and y-intercept (0,6).
Suppose 200=100e0.12t. Solve for t. Round to the third decimal place.
t=(ln 2)/0.12, which is approximately 5.776.
A function is said to be __________________ if every element from the range comes from exactly one element in the domain.
ONE-TO-ONE
Find the x-intercept and y-intercept of of f(x)=1/2x+1
x-int: (-2,0)
y-int: (0,1)