F-BF. Building Functions

F-BF.A. Build a function that models a relationship between two quantities.

• Exponential Parameters

F-BF.A.1. Write a function that describes a relationship between two quantities.

• 1,000 is half of 2,000
• A Sum of Functions
• Kimi and Jordan
• Lake Algae
• Skeleton Tower
• Summer Intern

F-BF.A.1.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.

• Compounding with a 100% Interest Rate
• Compounding with a 5% Interest Rate
• Susita's Account
• The Canoe Trip, Variation 1
• The Canoe Trip, Variation 2

F-BF.A.1.b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

• 1,000 is half of 2,000
• A Sum of Functions

F-BF.A.1.c. Compose functions. For example, if $T(y)$ is the temperature in the atmosphere as a function of height, and $h(t)$ is the height of a weather balloon as a function of time, then $T(h(t))$ is the temperature at the location of the weather balloon as a function of time.

• Building an Explicit Quadratic Function by Composition
• Crude Oil and Gas Mileage
• Flu on Campus
• Graphs of Compositions
• Temperature Conversions

F-BF.A.2. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

• Snake on a Plane

F-BF.B. Build new functions from existing functions.

• A Saturating Exponential

F-BF.B.3. Identify the effect on the graph of replacing $f(x)$ by $f(x) + k$, $k f(x)$, $f(kx)$, and $f(x + k)$ for specific values of $k$ (both positive and negative); find the value of $k$ given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

• Building a General Quadratic Function
• Building an Explicit Quadratic Function by Composition
• Building a quadratic function from $f(x) = x^2$
• Exploring Sinusoidal Functions
• Identifying Even and Odd Functions
• Identifying Quadratic Functions (Standard Form)
• Identifying Quadratic Functions (Vertex Form)
• Medieval Archer
• Transforming the graph of a function

F-BF.B.4. Find inverse functions.

• Invertible or Not?
• US Households

F-BF.B.4.a. Solve an equation of the form $f(x) = c$ for a simple function $f$ that has an inverse and write an expression for the inverse. For example, $f(x) =2 x^3$ or $f(x) = (x+1)/(x-1)$ for $x \neq 1$.

• Temperature Conversions
• Temperatures in degrees Fahrenheit and Celsius

F-BF.B.4.b. Verify by composition that one function is the inverse of another.

• Exponentials and Logarithms II

F-BF.B.4.c. Read values of an inverse function from a graph or a table, given that the function has an inverse.

• Latitude
• Rainfall

F-BF.B.4.d. Produce an invertible function from a non-invertible function by restricting the domain.

• No tasks yet illustrate this standard.

F-BF.B.5. Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

• Exponential Kiss
• Exponentials and Logarithms I