Transformations
Vertical Shift by c units
A function is invertible if:
Each output has exactly one input; the function has the property that is 1-1
Domain of exponential functions:
(-∞,∞), All reals, ℝ
Write the definition of Exponential functions
f(x)=ax
What is the average rate of change formula?
| = | f(b)-f(a) |
| b-a |
For the function f(x), t(x+c) represents this transformation.
Horizontal Shift by -c
The point (-1,2) is on f(x). Where is the equivalent point on f-1(x)?
(2,-1)
Range of exponential functions
(0,∞) {y|0<y}
Write the compound interest formula
A=P(1+r)t
Find the average rate of change on f(x)=x2x as x goes from 1 to 3
f(1) = 2, f(3) = 24
| 11= | 24-2 |
| 3-1 |
For the function f(x), c*t(x) represents this transformation.
Vertical Strech by a factor of c units.
The function f(x) has a Domain of [-3,9) and a Range of [-4,5). What are the Doman and Range of f-1(x)
Domain f-1(x): [-4,5)
Range f-1(x): [-3,9)
Name two points on a graph of exponential functions (form: f(x)=ax) used to find the model.
(0,1) and (1, a)
Write the continuous interest formula
A=Pert
Find the average rate of change on f(x)=πx-π-x as x goes from -6 to -4
Round to three decimal places.
f(-6) = -961.388, f(-4) = -97.399
| 431.995= | -97.399-(-961.388) |
| -4-(-6) |
For the function f(x), t(cx) represents this transformation.
Horizontal Stretch by a factor of 1/c
What is the inverse of f(x)=2x+3
f-1(x)=(x-3)/2
What does y=0 represent?
Horizontal Asymptote
Give examples of even and odd power functions
Bonus: include graphical symmetry for each
Even: ex: x2, x4, x6...; symmetric with respect to the y-axis;
Odd: ex: x3, x5, x7...; symmetric with respect to the origin; point (0,0);
You are driving from Tacoma to visit the Oregon State Marine Science Center in Newport, OR. You leave Tacoma at 6am to beat traffic and you arrive at noon. When you leave your odometer says 103,846 and when you arrive it says 104125. What was your average speed on the trip?
| 46.5mph= | 104125-103846 miles |
| 12-6 hours |
Name all transformations in the function f(x)=a*t(b(x+c/b))+d
What is the inverse of f(x)=4+√(2x-9)
| f-1(x)= | (x-4)2+9 |
| 2 |
What term describes exponential functions? or What is the relationship of the inputs and outputs of an exponential function?
1:1, 1-1, one-to-one
Write the three definitions of logs
log v = u exactly when v=10u
logb v = u exactly when v=bu
ln v = u exactly v=eu
Find the average rate of change on f(x)=xlog(x) as x goes from 1 to 9
Round to four decimal places.
f(1) = 0, f(9) = 8.5882
| 1.0735= | 8.5882-0 |
| 9-1 |