Functions and Graphing Quiz

Swimming Pool Rental

• A swimming pool can be rented for $110 per hour.
• The rental is for either 1 hour or 2 hours.
• The cost to rent the pool is a function of the number of hours.

Athlete's Run

• An athlete ran at a constant speed for 12 seconds.
• The graph shows the distance (in yards) the athlete ran as a function of time (in seconds).
• The data points on the graph are plotted to estimate different time values and the corresponding distance ran by the athlete.

Concert Tickets

• The total cost for x tickets to a concert includes a flat fee for processing.
• The cost per ticket is also present.
• One customer bought 4 tickets for $160.
• Another customer bought 8 tickets for $300.
• A linear equation will represent total cost in dollars (y) for x tickets.

Graphing Functions

• A graph represents the relationship between points on the x-y axis,
• different linear equations might represent different functions,
• The slope and y-intercept can be used to identify specific functions.
• A graph is visually represented to determine a suitable function represented in each case.

Solving Equations

• An equation (m-9) = (m-27) is given to find the value of m.
• An equation (7w - 2(w – 9) = 4 – 8(w + 2)) is given to solve for the value of w.
• Given expressions have been provided for finding solution sets.

Hot Dogs and Popcorn

• Hot dogs and popcorn are sold at a concession stand.
• Two families bought different amounts, at different prices,
• Determining the price of a hot dog and a bag of popcorn.
• System of equations with the given information are provided to determine the price of each.

Linear Inequalities

• Finding the solution set for the inequality y ≥ x – 2.

Coffee and Doughnuts

• Two customers purchased coffee and doughnuts.
• Each cup of coffee and each doughnut cost the same amount.
• The first customer paid $4.90 for 1 cup of coffee and 2 doughnuts.
• The second customer paid $8.60 for 2 cups of coffee and 3 doughnuts.
• Finding the cost of 1 cup of coffee.

Systems of Equations

• A system of equations, where 6x - 2y = 10 and y = 3x - 5, is given to find if there is one solution, no solution, or infinite solutions.
• The statement related to a system of equations explains different conditions under which a solution exists or not.
• The properties of equivalent functions are provided to ascertain a similar function.

Factoring Expressions

• Factoring an expression like x² + 7x – 30 determines a factor of the expression.

Simplifying Expressions

• Finding an equivalent expression to (6x²y)²(2x³y⁴).
• Finding an equivalent expression to (16km²)/(4k³m¹⁴).

Function Evaluation

• If f(x) is defined as a quadratic equation, evaluate f(4).