Unit 1
A number written in the form a+bi.
What is a complex number?
The process of using the output of one function as the input of another function.
What is composition of functions?
This inverse relationship exists between logarithmic and exponential functions.
What are inverse functions?
When multiplying a complex number by its conjugate, the result is always this type of number.
The result of (4+3i)+(2-5i).
Given f(x)=2x+1 and g(x)=x2, the value of (f∘g)(3).
What is 19?
The value of log2(32).
Given f(x)=x−4 and g(x)=3x, this is the value of (g∘f)(2).
The value of i2 used when multiplying complex numbers.
What is -1?
A function made up of two or more rules, where different rules are used for different input values.
This logarithm has a base of e≈2.718.
What is the natural logarithm (ln or loge)?
For a piecewise function, this quantity may change from one interval to another because each interval has its own rule.
The steps to find out the value of AB21 in matrix multiplication, where A & B are both 2x2 matrices.
On a graph of a piecewise function, this type of circle indicates that an endpoint is included in the domain of that piece.
What is a closed circle (closed dot)?
A population follows the model P=500(1.08)t. If the population reaches 1,000, this operation is needed to solve for t.
What is taking a logarithm of both sides?
A regression model predicts a value of 52 and the residual is −7. This was the actual value observed.
What is 45?
This geometric method uses a parallelogram to find the sum of two vectors.
What is the Parallelogram Rule of Vector Addition?
A regression model predicts a value of 42, but the actual value is 37. Using the residual formula, calculate the residual and explain what it means.
What is −5, meaning the model overpredicted the value by 5?
An account earns 5% annual interest compounded monthly. If $4,000 is invested and grows to $6,000, approximately how many years will it take for this to happen.
What is t≈8.1 years?
A bacteria culture follows the model P=800(0.92)t. After approximately how many days, the population falls to 400 bacteria. (Round to 1 decimal place)
What is t≈8.3 days?