MATHS Targeted Standards (A) Concept: Algebra (REI) Domain: Reasoning with Equations and Inequalities Cluster: Represent and solve equations and inequalities graphically
MATHS.AREI.11 Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Note: In Algebra I, only linear and exponential will be the focus.
Student Learning Targets:
Knowledge Targets
I can
I can
Reasoning Targets
I can explain why the intersection of y = f(x) and y = g(x) is the solution of f(x) = g(x) for any combination of linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Skills (Performance) Targets
I can use technology to graph the equations and find their points of intersection.
I can use tables of values or successive approximations to find solutions.
Product Targets
I can
I can
Proficiency Scale
Score
Description
Sample Activity
4.0
In addition to achieving level 3.0 content, the student makes indepth inferences and applications that go beyond what was taught
On the graphs of f(x) and g(x), interpret where f(x)>g(x)or where f(x)<g(x)
3.5
In addition to Score 3.0 performance, the student demonstrates indepth inferences and applications regarding the more complex content with partial success.
3.0
The student can:
explain why the intersection of y = f(x) and y = g(x) is the solution of f(x) = g(x) for any linear or exponential functions.
use technology and tables to graph the equations and find their points of intersection
use tables of values or successive approximations to find solutions
The student exhibits no major errors or omissions.
Use a graphing calculator to find and justify the approximate solution(s) to the system below.
f(x)=x+4 g(x)=4x
Solutions: x= 0
f(0) = 4 and g(0)=4
Given the following system, for what x value(s), is f(x) = g(x)?
Solutions: x=1
Because f(1) = 5 and g(1) = 5
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 can:
recognize and recall basic vocabulary, such as:
function notation
solution
xcoordinate
linear function
exponential function
evaluate using function notation and order of operations.
identify the intersection of two functions.
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.
Find the value of f(4). if f(x)=3x+7.
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.

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).