Semester 1 Review

Front

What is the function to find t, the total number of gallons of water in an aquarium after w weeks if it starts with 275 gallons and decreases at a rate of 15 gallons per week?

Back

t = -15w + 275

Front

What does it mean for a graph to represent y as a function of x?

Back

A graph represents y as a function of x if each x corresponds with exactly 1 y.

Front

Identify a situation that is not proportional: The number of gallons of water in x barrels with 42 gallons each, the earnings of an employee at $8.50 per hour for h hours, the weight of a puppy gaining 2 pounds per week starting at 8 pounds, or the cost of p pounds of bananas at $0.55 per pound.

Back

The weight of a puppy gaining 2 pounds per week starting at 8 pounds is not proportional.

Front

If a circle is reflected across the y-axis, what is the new center if the original center was at (x, y)?

Back

The new center is at (-x, y).

Front

What type of transformation is described by the rule (x,y) → (-x, -y)?

Back

A 180 degree clockwise rotation around the origin.

Front

Define a function in mathematical terms.

Back

A function is a relation where each input (x) has exactly one output (y).

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities maintain a constant ratio.

Front

How do you determine if a relation is a function using the vertical line test?

Back

If a vertical line intersects the graph at more than one point, the relation is not a function.

Front

What is the formula for the area of a circle?

Back

The area of a circle is A = πr², where r is the radius.