ACP Review: Day 1

Front

What does it mean for a quantity to vary directly with another?

Back

A quantity varies directly with another if it increases or decreases in proportion to that quantity. This relationship can be expressed with the equation y = kx, where k is a constant.

Front

If 5.5 gallons of gas cost $12.60, how do you find the cost per gallon?

Back

To find the cost per gallon, divide the total cost by the number of gallons: Cost per gallon = Total cost / Gallons = $12.60 / 5.5 = $2.40.

Front

What is the equation that represents the total cost of gas if it varies directly with the amount purchased?

Back

The equation is y = 2.40x, where y is the total cost and x is the number of gallons.

Front

What is a y-intercept in a graph?

Back

The y-intercept is the point where the graph intersects the y-axis, representing the value of y when x = 0.

Front

In the context of weight loss, what does a constant rate mean?

Back

A constant rate means that the amount lost is the same over equal intervals of time, resulting in a straight line when graphed.

Front

What does the point (0,10) represent in a weight loss graph?

Back

The point (0,10) indicates that at the start (week 0), Jonathon weighed 10 pounds more than his target weight.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Given the range -5 < y ≤ 7, what does this indicate about the function's outputs?

Back

This indicates that the function's outputs can be greater than -5 but less than or equal to 7.

Front

How do you determine the range of a function from a graph?

Back

To determine the range from a graph, identify the lowest and highest y-values that the graph reaches.

Front

What is the difference between an open interval and a closed interval?

Back

An open interval does not include its endpoints (e.g., (a, b)), while a closed interval includes its endpoints (e.g., [a, b]).