Key Takeaways
- Know how to move among equations, graphs, tables, and verbal descriptions of functions.
- Compare linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric behavior quickly.
- Interpret transformations, inverses, composition, rate of change, and average rate of change with precision.
- In calculus, focus on limit ideas, derivative meaning, graphical interpretation, and basic antiderivative reasoning.
- Teaching questions often ask which representation best reveals growth, concavity, slope behavior, or asymptotes.
Last updated: March 2026
Domain Strategy
The functions and calculus domain rewards interpretation, not just computation. You need to see how a function behaves and explain what that behavior means.
Function Priorities
Review:
- domain and range
- function notation and evaluation
- intercepts, zeros, extrema, and asymptotes
- composition and inverse relationships
- transformations of parent functions
- exponential versus linear growth
- logarithms as inverses of exponentials
- trigonometric ratios, graphs, period, and amplitude
Calculus Priorities
You do not need a full university calculus sequence. Praxis 5165 is more focused on:
- limit intuition and continuity
- derivative as instantaneous rate of change and slope
- using derivative sign to describe increasing and decreasing behavior
- interpreting concavity from derivative information
- basic antiderivative and accumulation ideas
High-Value Exam Habit
When you read a function question, ask:
- What representation am I given?
- What feature am I actually being asked about?
- Would a graph, symbolic rewrite, or numerical estimate make the structure clearer?
Test Your Knowledge
If f(x) = 2x^2 - 3x + 1, what is f(2)?
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Test Your Knowledge
What is the best interpretation of the derivative of a position function s(t)?
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