ALG2.MATH.2.A
Graph the functions f(x)=√x, f(x)=1/x, f(x)=x3, f(x)= 3√x, f(x)=bx, f(x)=|x|, and f(x)=logb: (x) Where b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval.
Algebra II · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012
Standard Unwrapping
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functionsgraphf(x)=√xf(x)=1/xf(x)=x3f(x)=3√xf(x)=bxf(x)=|x|f(x)=logb(x)b (2, 10, e)key attributesdomainrangeinterceptssymmetriesasymptotic behaviormaximumminimuminterval
Skills
- graph (various parent functions, including radical, rational, cubic, cube root, exponential, absolute value, and logarithmic with specified parameters) #dok2
- analyze (key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and extrema for the given functions) #dok2
- identify (domain and range for different functions over specified intervals) #dok1
- determine (maximum and minimum values on a given interval) #dok2
- compare (key attributes among different types of functions) #dok2
Learning Targets
- I can identify the domain and range of various parent functions. #dok1
- I can describe intercepts and symmetries for specific functions. #dok1
- I can graph f(x) = √x, 1/x, x3, 3√x, bx, |x|, and logb(x) for specified values of b. #dok2
- I can determine intervals where a function has maximum or minimum values. #dok2
- I can analyze asymptotic behavior in rational and exponential/logarithmic functions. #dok2
- I can compare the key attributes of different parent functions. #dok2
- I can explain how changing the interval affects the observed maximum or minimum values in a function. #dok3
- I can justify the classification of function key attributes with reference to their algebraic definitions and graphs. #dok3
Big Ideas
- Different types of functions each have unique key attributes that can be analyzed and compared across graphs.
- Understanding the graphical and algebraic properties of parent functions helps identify their real-world applications and connections.
Essential Questions
- How do key attributes such as domain, range, and asymptotes differ among various parent functions?
- What patterns can you observe in the graphs of f(x) = √x, 1/x, x3, 3√x, bx, |x|, and logb(x)?
- How do you determine the maximum and minimum values of a function on a specific interval?
- Why is it important to analyze the symmetries and asymptotic behavior of functions?
- In what real-world contexts might these different parent functions and their attributes appear?