Content Standard(s):
Mathematics 34 ) 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.
[F-BF3]
Mathematics 34 ) 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.
[F-BF3]
Mathematics 22. 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 explain the effects on the graph using technology, where appropriate. Limit to linear functions. [Algebra I with Probability, 23]
Unpacked Content
Evidence Of Student Attainment:
Students:
Find k values when given the graphs of linear functions or when expressed in the forms f(x) + k. k(f(x)). f (kx). and f (x +k).
Use appropriate technology to experiment with these cases to verify the effects of manipulating k values for linear functions. Teacher Vocabulary:
Linear function
Slope
y-intercept Knowledge:
Students know:
Linear relationships have input and output values that have an associated graph, including a y-intercept.
parallel lines have the same slope but different y-intercepts. Skills:
Students are able to:
Compare functions with the same slopes graphically while manipulating k values.
Explore functions with a calculator or graphing software to develop a relationship
between the coefficient on x and the slope. Understanding:
Students understand that:
Linear functions can shift based on factors other than the independent variable.
The shift of a function is not the same as the stretch of a function. Diverse Learning Needs:
Mathematics 23. Identify the effect on the graph of replacing f(x) by f(x)+k,k·f(x), f(k·x), 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 explain the effects on the graph, using technology as appropriate. Limit to linear, quadratic, exponential, absolute value, and linear piecewise functions.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given a function in algebraic form,
Graph the function, f(x), conjecture how the graph of f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k(both positive and negative) will change from f(x), and test the conjectures.
Describe how the graphs of the functions were affected (e.g., horizontal and vertical shifts, horizontal and vertical stretches, or reflections).
Use technology to explain possible effects on the graph from adding or multiplying the input or output of a function by a constant value. Given the graph of a function and the graph of a translation, stretch, or reflection of that function, determine the value which was used to shift, stretch, or reflect the graph. Teacher Vocabulary:
Composite functions
Horizontal and vertical shifts
Horizontal and vertical stretch
Reflections
Translations Knowledge:
Students know:
Graphing techniques of functions.
Methods of using technology to graph functions Skills:
Students are able to:
Accurately graph functions.
Check conjectures about how a parameter change in a function changes the graph and critique the reasoning of others about such shifts.
Identify shifts, stretches, or reflections between graphs. Understanding:
Students understand that:
Graphs of functions may be shifted, stretched, or reflected by adding or multiplying the input or output of a function by a constant value. Diverse Learning Needs:
Essential Skills:
Learning Objectives: ALGI.23.1: Define dilation, rotation, reflection, translation, congruent and sequence.
ALGI.23.2: Identify rotations.
ALGI.23.3: Identify reflections.
ALGI.23.4: Identify translations.
ALGI.23.5: Use digital tools to formulate solutions to authentic problems (Ex: electronic graphing tools, probes, spreadsheets).
Prior Knowledge Skills:
Identify congruent figures.
Compare rotations to translations.
Compare reflections to rotations.
Compare translations to reflections.
Recognize translations (slides), rotations (turns), and reflections (flips).
Alabama Alternate Achievement Standards
AAS Standard:
