Linear Functions
What is the general form of a linear function?
y=mx+b
What is the general form of an exponential function?
y=a⋅bx
What is the standard form of a quadratic function?
y=ax2+bx+c
What is the formula for simple interest?
y= mx + b
Solve for x: 2x+3=7
x=2
How do you identify the slope of a linear function from its graph?
The slope of a linear function can be identified as the rise over run between two points on the graph, or the coefficient of x in the equation y=mx+b
How does the graph of an exponential function behave as x increases?
As x increases, the graph of an exponential function either grows rapidly (exponential growth) or decreases rapidly (exponential decay).
How can you find the vertex of a quadratic function from its graph?
The vertex of a quadratic function can be found by looking at the highest point (maximum) or the lowest point (minimum).
How does compound interest differ from simple interest?
Compound interest differs from simple interest in that compound interest is calculated by multiplying a constant rate and simple interest is calculated by adding a constant.
What is the slope-intercept form of a linear equation?
The slope-intercept form of a linear equation is y=mx+b
If a linear function has a slope of 2 and passes through the point (1,3), what is its equation?
The equation of the linear function is y=2x+1.
If an exponential function grows by a factor of 3 for each unit increase in x, what is its equation?
y=3x
What is the shape of the graph of a quadratic function?
The shape of the graph of a quadratic function is a parabola.
Calculate the total amount using compound interest for a principal of $1000, an interest rate of 5%, compounded annually for 3 years.
$1157.63
Simplify the expression: 3(x−4)+2x
5x−12
Describe a real-world situation that can be modeled by a linear function.
Sample Response: A real-world situation that can be modeled by a linear function is calculating the total cost of items where each item has a fixed price.
Describe a real-world situation that can be modeled by an exponential function.
Sample Example: A real-world situation that can be modeled by an exponential function is population growth where the population doubles every fixed period.
If a quadratic function opens downwards, what can you say about its leading coefficient?
If a quadratic function opens downwards, the leading coefficient a is negative.
What is the formula for compound interest?
A=P(1+r/n)nt
Solve the system of equations: y=2x+1 and y=−x+4
x=1, y=3
What are the characteristics of the graph of a linear function?
The characteristics of the graph of a linear function include a straight line with a constant slope, and it can be increasing, decreasing, or horizontal.
What is the difference between a growth and decay exponential function?
The difference between a growth and decay exponential function is that in growth, the base b is greater than 1, while in decay, the base bb is between 0 and 1.
Give an example of a real-world scenario that can be modeled by a quadratic function.
Sample Response: A real-world scenario that can be modeled by a quadratic function is the trajectory of a projectile, such as a ball being thrown.
How does changing the compounding interval affect the total interest earned on an investment?
Changing the compounding interval affects the total interest earned on an investment by increasing the frequency of interest calculation, which results in more interest being earned.
Factor the quadratic expression: x2−5x+6x
The factored form of the quadratic expression is (x−2)(x−3)