More Language of Algebra (Basics)

The Commutative and Associative Properties can be used with other properties when evaluating and simplifying expressions.

Use the expression four times the sum of a and b increased by twice the sum of a and 2b.

The return of normal blood flow to the brain is said to be a function of the number of days since the concussion.

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Each input x and its corresponding output y can be represented on a graph using ordered pairs. Ordered Pair X & Y Coordinates

In Example 1, the percent of normal blood flow depends on the number of days from the injury. Independent Dependent Independent

Identify the independent and dependent variables for each function. a. In general, the average price of gasoline slowly and steadily increases throughout the year. Time is the independent variable as it is unaffected by the price of gasoline, and the price is the dependent quantity as it is affected by time.

B) The profit that a business makes generally increases as the price of their product increases. In this case, price is the independent quantity. Profit is the dependent quantity as it is affected by the price.

The graph represents the speed of a school bus traveling along its morning route. Describe what is happening in the graph.

At the origin, the bus is stopped. It accelerates and maintains a constant speed. Then it begins to slow down, eventually stopping. After being stopped for a short time, the bus accelerates again. The starting and stopping process repeats continually.

b. Identify the graph that represents the altitude of a space shuttle above Earth, from the moment it is launched until the moment it lands. Before it takes off, the space shuttle is on the ground. It blasts off, gaining altitude until it reaches space where it orbits Earth at a constant height until it comes back to Earth. Graph A shows this situation.

An electronics store is having a special sale. For every two DVDs you buy at the regular price of $29 each, you get a third DVD free. b. Write the data as a set of ordered pairs. a. Make a table showing the cost of buying 1 to 5 DVDs.

c) Draw a graph that shows the relationship between the number of DVDs and the total cost.

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Rasha earns $6.75 per hour working up to 4 hours each day after school. Her weekly earnings are a function of the number of hours she works. a. Identify a reasonable domain and range for this situation.

b. Draw a graph that shows the relationship between the number of hours Rasha works and the amount she earns each week.

Practice

Paul is a pitcher for his school baseball team. Draw a reasonable graph that shows the height of the baseball from the ground from the time he releases the ball until the time the catcher catches the ball. Let the horizontal axis show the time and the vertical axis show the height of the ball. Time Height

Michelle gets a fever and takes some medicine. After awhile her temp comes down, then slowly begins to go up again

His account is increasing as he makes deposits and earns interest. Then he pays some bills. He then makes some deposits and earns interests, and so on.