MAT-HS.F-IF.08
MAT-HS Targeted Standards (F) Concept: Function (IF) Domain: Interpreting Functions Cluster: Analyze functions using different representations
MAT-HS.F-IF.08 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
- b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
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Student Learning Targets:
Knowledge Targets
- I can recall the order of operations.
- I can understand and identify a power and its parts (base and exponent).
- I can recognize the properties of exponents (i.e. product of powers, power of a power, power of a product).
- I can recognize a zero or negative exponent.
- I can identify a radical.
- I can identify if a radical expression is in simplest form.
- I can recognize the properties of radicals, i.e., product, quotient, and sum of radicals.
- I can identify perfect squares.
- I can define a logarithm.
- I can recall properties of logarithms and exponents.
- I can recognize common logarithms and natural logarithms.
- I can identify an asymptote.
- I can recall the change of base formula.
Reasoning Targets
- I can analyze an algebraic expression.
- I can decide what to do next based on my knowledge of the order of operations.
- I can distinguish the difference of when to use each property of radicals.
- I can evaluate the properties of radicals.
- I can apply the distributive property.
- I can analyze what type of factoring technique that should be used for a given expression. (i.e. factor trinomials, factor difference of squares, factor sum and difference of cubes, factor by grouping, factor out the greatest common factor)
- I can combine like terms in an expression or equation.
- I can convert from a logarithm to exponential expressions.
- I can identify an asymptote.
- I can expand and condense logarithms.
- I can evaluate logarithms and exponential expressions.
- I can distinguish between a natural log and common log.
Skills (Performance) Targets
- I can simplify an algebraic expression.
- I can apply factor using perfect square.
- I can do prime factorization.
- I can rationalize a denominator.
- I can simplify a polynomial expression.
- I can multiply polynomials.
- I can justify the steps taken in manipulating an expression.
- I can complete all necessary steps in order to simplify the expression.
- I can distribute and factor an expression.
- I can solve for (isolate) a specific variable.
- I can perform transformations that produce equivalent equations (e.g., adding the same amount to both sides of the equation, etc.).
- I can check the solution.
- I can set a polynomial equal to zero and solve by factoring, quadratic formula, graphing, linear combinations, and substitution.
- I can solve for (isolate) a specific variable.
- I can write a linear system.
- I can perform transformations that produce equivalent equations (e.g., adding the same amount to both sides of the equation, etc.)
- I can check the solution.
- I can solve a quadratic.
- I can multiply and factor polynomials.
- I can solve a linear inequality.
- I can graph a linear inequality.
- I can solve a system of linear inequalities.
- I can graph a system of linear inequalities.
- I can check the solution of the system.
- I can solve a linear system (substitution, linear combination, graphically).
- I can write a linear system.
- I can identify the number of solutions of a linear system.
- I can identify the most efficient method to solve a system.
- I can check the solution of the system.
- I can apply basic properties of exponents and logarithms to rewrite algebraic expressions.
- I can graph logarithmic and exponential functions.
- I can solve logarithmic and exponential equations.
- I can apply the change of base formula to evaluate a logarithmic expression.
- I can graph and determine the equation of an asymptote.
- I can write a function in equivalent forms (eg. factored vs. general form) to show different properties of the function.
- I can explain different properties of a function that are revealed by writing a function in equivalent forms.
- I can use the process of factoring and completing the square in a quadratic function to show zeros, a maximum or minimum, and symmetry of the graph, and interpret these in terms of a real-world situation.
- I can use the properties of exponents to interpret exponential functions as growth or decay.
Product Targets
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Proficiency Scale
Score |
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Description |
Sample Activity
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4.0 |
In addition to achieving level 3.0 content, the student makes in-depth inferences and applications that go beyond what was taught |
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
3.0 |
The student can:
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Write a function in equivalent forms (eg. factored vs. general form) to show different properties of the function
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Explain different properties of a function that are revealed by writing a function in equivalent forms
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Use the process of factoring and completing the square in a quadratic function to show zeros, a maximum or minimum, and symmetry of the graph, and interpret these in terms of a real-world situation
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Use the properties of exponents to interpret exponential functions as growth or decay
The student exhibits no major errors or omissions. |
Given f(x)=x2-5x-6:
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Rewrite the function in factored form to find the zeros.
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Find the x value of the maximum or minimum and state if a maximum or minimum occurs at that x value.
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
2.0 |
There are no major errors or omissions regarding the simpler details and processes as the student:
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. |
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
1.0 |
With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. |
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
Alg II Equivalent Quadratic Expressions Proficiency Scale
Score |
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Description |
Sample Activity
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4.0
(advanced)
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In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. |
Write the equation of the following graph in the three forms. If you cannot write the function in one of the forms, explain why.
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3.5 |
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. |
3.0
(proficient)
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The student can:
- explain the different properties of a function that are revealed by writing a function in equivalent forms.
- write a function in equivalent forms (factored vs. general form) to show different properties of the function.
The student exhibits no major errors or omissions. |
Rewrite the following equation of the parabola in vertex form. Identify the minimum/maximum value.
f(x)=2x2+16x+10
Rewrite the following equation of the parabola in standard form and find the vertex.f(x)=2(2x-1)(x+9)
Explain the advantages of each form of a quadratic function.
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2.5 |
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). |
2.0
(progressing)
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There are no major errors or omissions regarding the simpler details and processes as the student can:
- identify the different forms of functions (eg. Factored vs. general form) that show different properties of the function.
- recognize and recall basic terminology, such as:
- factor
- intercept
- vertex
- complete the square
- standard form
- parabola
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.
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Label each of the following functions with the quadratic form it represents.
- f(x)=2x2+5x+9
- q(x)=3(2x+5)(x-2)
3. g(x)=4(x-3)2+6 |
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1.5 |
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). |
1.0
(beginning)
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With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). |
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0.5 |
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). |
0.0 |
Even with help, the student demonstrates no understanding or skill. |
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Resources
Web
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Vocab
- exponential growth
- exponential decay
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