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