Logarithms
What is the base of log(x)?
10
Rewrite 3(x+4) = 9 in logarithmic form.
log39 = x+4
What is the parent function for a rational function?
y = 1/x or f(x) = 1/x
(0,infinity)
What is ln(x) equivalent to?
loge(x)
What is the asymptote for the function of f(x)= 2x?
Horizontal, y=0
What kind of asymptote(s) do rational functions have?
Horizontal and Vertical
For regression, we look for our r2 to be as close as possible to ____.
1
Rewrite log4(x-6) = 3 in exponential form.
43 = x-6
Describe what happens to f(x) = 5x when it is replaced with -f(x-3)+6
Reflected
Right 3
Up 6
f(x)=1/x is transformed into g(x)= 4/(x-8). Describe the transformations.
Vertical stretch by 4
Horizontal shift right 8 units
Simplify (16 - i ) + 4i(2 + i).
i = sqrt(-1) i2 = -1
7i + 12
Solve ln(x+1)=4
x = e4 - 1
An initial deposit of $2,000 was deposited into a savings account that earns 3 percent annual interest compounded continuously.
Which equations represents the balance after t years?
Continuous Compound
A = 2000e.03t
A train traveled 50 miles in the same amount of time it took a bus to travel 15 miles. The train's speed was 45 mph faster than the bus' speed.
Which equation will be used to calculate the speed of each?
Train Bus
50 = 15
x+45 x
How do you find the intersection of two functions on the calculator? What steps?
Menu, 6, 4
Where is the asymptote shifted in the function g(x)=ln(x+5)+3?
The VERTICAL asymptote is shifted 5 units left.
A business owner has an loan balance of $2,000. Their amount of left on the loan decreases yearly by 30 percent.
Which equation represent the amount left on their balance after t years?
Compound
A = 2000(0.7)t or A = 2000(1-0.3)t
Add.
3 = 1
x+3 x+4
4x+15
(x+3)(x+4)
What line do inverses always reflect over?
y=x (diagonal)