Learning Goal
Finding and verifying inverse functions
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
- Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
- Guided Notes →One page your students fill in and keep.
- Exit Ticket →Three items at the end of class. No student accounts.
- Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
- Homework →Assign practice; it grades itself.
**G 607.** Find the coordinates of a point reflected across a vertical or horizontal line or across y = x
**A 601.** Manipulate expressions and equations
**A 403.** Solve routine first-degree equations
**F 604.** Evaluate composite functions at integer values
**F 707.** Exhibit knowledge of logarithms
**F 505.** Understand the concept of a function as having a well-defined output value at each valid input value
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G 607. Find the coordinates of a point reflected across a vertical or horizontal line or across y = x
A 601. Manipulate expressions and equations
A 403. Solve routine first-degree equations
F 604. Evaluate composite functions at integer values
F 707. Exhibit knowledge of logarithms
F 505. Understand the concept of a function as having a well-defined output value at each valid input value
What you'll learn
- Define the inverse of a function as the rule that reverses its input-output pairing, and explain why $f^{-1}$ does not mean $\frac{1}{f}$
- Find $f^{-1}(x)$ for a linear function by swapping $x$ and $y$ and solving for $y$, and explain why the swap comes first
- Verify a claimed inverse by composing in both orders and obtaining $x$, and reject a claim when a composition fails
- Sketch $f^{-1}$ by reflecting the graph of $f$ across the line $y = x$, using the point rule $(a,b) \mapsto (b,a)$
- State the domain and range of $f^{-1}$ from those of $f$
- Decide whether a function has an inverse function by applying the horizontal line test, and explain what the test is checking
Slides
Step through the lesson, or watch it as a narrated video
Slides
In development
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