1. Plot the data. 2. Determine if a linear relationship exists. 3. Find the slope and y-intercept. 4. Write the equation in slope-intercept form: $y = mx + b$.

1. Plot the data. 2. Choose a polynomial degree based on the shape. 3. Use a calculator to perform polynomial regression. 4. Write the resulting equation.

1. Identify the intervals. 2. Determine the function for each interval. 3. Write the function with the corresponding domains.

1. Identify any restrictions on the input variable (e.g., values that make the denominator zero). 2. Consider the physical limitations of the scenario (e.g., non-negative quantities). 3. Determine the possible output values based on the restricted domain.

1. Identify the inversely proportional quantities. 2. Write the general form of the rational function: $y = \frac{k}{x}$. 3. Use given data to find the constant of proportionality, $k$. 4. Write the specific equation and use it to solve for the unknown.

1. Identify the interval in which the point lies. 2. Use the function defined for that interval to calculate the value.

1. Calculate the total volume of the tank. 2. Divide the total volume by the filling rate to find the time.

1. Start with the parent function. 2. Apply transformations step-by-step, writing the equation as you go. 3. Simplify the final equation.

1. Plot the data. 2. Look for patterns (straight line, curve, rapid growth/decay, inverse relationship). 3. Consider the real-world context. 4. Use regression to test different models.

1. Identify the units of each variable. 2. Make sure the units are consistent throughout the problem. 3. Include the correct units in your final answer.

It indicates a value where the function is undefined, often due to division by zero. The function approaches infinity (or negative infinity) as x approaches that value.

The graph will consist of different function segments connected or disconnected at specific points, each corresponding to a different interval.

The graph stretches away from the origin. Larger $k$ values mean that for the same $x$, $y$ is larger, and vice versa.

It indicates the value that the function approaches as x goes to positive or negative infinity. This represents a limit on the output of the function.

Look for shifts (left/right, up/down), stretches/compressions (narrower/wider, taller/shorter), and reflections (across x or y axis) compared to the parent function's graph.

It indicates a point where the function is not continuous, which can be a hole, a jump, or a vertical asymptote.

The slope represents the rate of change of the function. A positive slope indicates an increasing function, a negative slope indicates a decreasing function, and a zero slope indicates a constant function.

The domain is the set of all x-values covered by the graph, and the range is the set of all y-values covered by the graph.

It tells you what happens to the function's values as x approaches positive or negative infinity. This is determined by the leading term of the polynomial.

Check if the function is continuous at the boundary points. If there's a jump or a break, the function is discontinuous at that point.

Linear: Straight line, constant rate of change | Polynomial: Curve, changing rate of change

Polynomial: Can be written as a sum of terms with non-negative integer exponents. | Rational: Written as a ratio of two polynomials, may have asymptotes.

Shifts: Translate the graph without changing its shape. | Stretches: Change the shape by compressing or expanding the graph.

Direct: As one quantity increases, the other increases. | Inverse: As one quantity increases, the other decreases.

Domain: Set of possible input values (x). | Range: Set of possible output values (y).

Continuous: A single function defined over its entire domain without any breaks. | Piecewise: Defined by different functions over different intervals of its domain.

Vertical Stretch: Multiplies the y-values by a factor, making the graph taller. | Horizontal Compression: Divides the x-values by a factor, making the graph narrower.

Vertical Shift: Moves the graph up or down by adding or subtracting a constant. | Horizontal Shift: Moves the graph left or right by adding or subtracting a constant from the x-value.

Linear Regression: Finds the best-fitting straight line for the data. | Polynomial Regression: Finds the best-fitting polynomial curve for the data.

Assumptions: Simplifications made about the real-world scenario to create a tractable model. | Restrictions: Constraints on the domain or range of the function based on the real-world context.