1a) identify and list features of a mathematical model given graphical form
b) Identify and list a minimum of three features of a mathematical model given an algebraic form.
c) identify and list a minimum of three features of mathematical model given in table of values.
a) To identify and list features of a mathematical model given graphical form, follow these steps:
1. Analyze the shape of the graph: Look for patterns, slopes, curves, or any other distinctive characteristics.
2. Identify key points: Pay attention to the x- and y-intercepts, maximums, minimums, inflection points, or any other important locations.
3. Determine the relationship between variables: If there are multiple lines or curves, analyze how they interact with each other.
4. Look for symmetry: Check if the graph is symmetric about the x-axis, y-axis, or origin.
5. Consider the boundaries: Assess any restrictions or limitations on the graph, such as asymptotic behavior or specific intervals.
b) To identify and list features of a mathematical model given an algebraic form, follow these steps:
1. Identify the variables and their roles: Determine which variables are dependent and independent, and understand their relationship.
2. Examine the coefficients and exponents: Observe the values and signs of the coefficients and exponents.
3. Assess the type of equation: Identify if it is linear, quadratic, exponential, logarithmic, trigonometric, etc.
4. Check for restrictions or limitations: Look for any domain or range restrictions, as well as asymptotic behavior or specific intervals.
5. Analyze special points or values: Identify any critical points, zeros, intercepts, or points of discontinuity.
c) To identify and list features of a mathematical model given in a table of values, follow these steps:
1. Observe the relationship between the inputs and outputs: Look for any patterns or trends that indicate dependence or change.
2. Determine the type of relationship: Assess if it is linear, exponential, quadratic, periodic, etc.
3. Examine the difference between consecutive values: Calculate the rate of change between consecutive inputs and outputs.
4. Identify any special values or points: Look for maximums, minimums, zeros, asymptotic behavior, or other significant values.
5. Consider the limitations or restrictions: Check for any domain or range restrictions, as well as any specific intervals where the model is valid.