The Inverse of a Rational Function

The graph models the number of hours$\left(y\right)$ it takes for aid workers $\left(x\right)$ to build a shelter for refugees.

From this graph, determine the rational function and hence explain how long it would take:

$10$ people to build the shelter.

Predict what transformation takes the graph of $y=\frac{1}{x}$ to the graph of $y=\frac{1}{x-2}+3$. What will be the equations of its asymptotes? Explain your reasoning.

For the function $y=f(x-h)+k$, describe the effects of the parameters $h$ and $k$ on the graph of $y=f\left(x\right)$. Use appropriate mathematical terms and demonstrate what you mean with an example.

How can understanding transformations of rational functions help you graph them?

Newton's second law of motion, $F=ma$, states the relationship between force, mass, and acceleration. Describe the proportional relationship between: acceleration and mass. Hence sketch graphs of: acceleration versus mass for a fixed force.

Newton's second law of motion, $F=ma$, states the relationship between force, mass, and acceleration. Describe the proportional relationship between: force and acceleration. Hence sketch graphs of: force versus acceleration for a fixed mass

Newton's second law of motion, $F=ma$, states the relationship between force, mass, and acceleration. Describe the proportional relationship between:

acceleration and mass

Newton's second law of motion, $F=ma$, states the relationship between force, mass, and acceleration. Describe the proportional relationship between:

force and acceleration

The graph models the number of hours$\left(y\right)$ it takes for aid workers $\left(x\right)$ to build a shelter for refugees.

From this graph, determine the rational function and hence explain how long it would take:

$5$ people to build the shelter.

The graph models the number of hours$\left(y\right)$ it takes for aid workers $\left(x\right)$ to build a shelter for refugees.

From this graph, determine the rational function and hence explain how long it would take:

$1$ person to build the shelter.

Below is the graph of the resistance in an electric circuit $\left(R\right)$ versus the current $\left(I\right)$ flowing through it for a constant voltage.

Write down the function relating current $\left(I\right)$ and resistance $\left(R\right)$.

Below is the graph of the resistance in an electric circuit $\left(R\right)$ versus the current $\left(I\right)$ flowing through it for a constant voltage.

Find the constant of proportionality using points from the graph.

Below is the graph of the resistance in an electric circuit $\left(R\right)$ versus the current $\left(I\right)$ flowing through it for a constant voltage.

Describe the relationship between current and resistance.

The length of time it takes to build a community shelter is inversely proportional to the number of people working on the project. It takes $600$ hours for $4$ people to build a shelter. Model this situation with a rational function. Determine how long it would take $12$ people to build a shelter.

The length of time it takes to build a community shelter is inversely proportional to the number of people working on the project. It takes $600$ hours for $4$ people to build a shelter. Model this situation with a rational function and sketch its graph.

Draw a graph of the following function and label the asymptotes: 

$y=-\frac{2}{3x}$.

State the domain and range of the function: $y=-\frac{2}{3x}$.

Draw a graph of the following function and label the asymptotes: 

$y=\frac{1}{4x}$.

State the domain and range of the function: $y=\frac{1}{4x}$.

Draw a graph of the following function and label the asymptotes: 

$y=-\frac{8}{x}$.