MA19.A2.14

Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.14
Explain why the x-coordinates of the points where the graphs of the equations $y = f(x)$ and $y = g(x)$ intersect are the solutions of the equation $f(x) = g(x)$.

Unpacked Content

Knowledge

Students know:

Defining characteristics of linear, polynomial, rational, absolute value, exponential, logarithmic graphs, radical, trigonometric (sine and cosine), and general piecewise functions.
Methods to use technology, tables, and successive approximations to produce graphs and tables for linear, polynomial, rational, absolute value, exponential, logarithmic, radical, trigonometric (sine and cosine), and general piecewise functions.

Skills

Students are able to:

Determine a solution or solutions of a system of two functions.
Accurately use technology to produce graphs and tables for linear, polynomial, rational, absolute value, exponential, logarithmic, radical, trigonometric (sine and cosine) and general piecewise functions.
Accurately use technology to approximate solutions on graphs.

Understanding

Students understand that:

When two functions are equal, the x coordinate(s) of the intersection of those functions is the value that produces the same output (y-value) for both functions.
Technology is useful to quickly and accurately determine solutions and produce graphs of functions.

Vocabulary

Functions
Successive approximations
Linear functions
Polynomial functions
Rational functions
Absolute value functions
Exponential functions
Logarithmic functions
Radical functions
Trigonometric (sine and cosine) functions
General piecewise functions

Design by Adaptive Theme