True/False Math 123 Functions + Linear Models

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false

A mathematical model can never be a linear function.

false

Every straight line has a slope.

false

Every straight line is the graph of a linear function of one variable.

false

If C is a cost function, then C(x) is the average cost of the first x items.

true

If C is a cost function, then C(x) is the total cost of x items.

true

If a is in the domain of f, then (a, f(a)) is a point of its graph.

true

If position is a linear function of time, then the slope of the graph represents the velocity

true

If the function f is given by f(x) = 2, then f(1) is defined.

false

If the total weekly revenue for items priced at $p is given by the function R(p) = −p2 + 100p, then the total weekly revenue will be $100 if we give the items away.

true

If the weekly sales q of an item priced at $p are given by q = −3p + 40, then the weekly sales decrease by 3 items for every $1 increase in price.

true

If y is a linear function of x, then y changes by a fixed amount for each increase of one unit in x.

false

In a linear cost function, the marginal cost and variable cost are equal.

false

In a linear cost function, the slope gives the total cost of one item.

true

In a linear demand function of the form q = mp + b we measure the slope in units of demand per unit of price.

false

In a linear demand function, the slope gives the demand of each additional item.

false

Some real-valued functions assign two or more values to certain numbers in their domains.

true

The graph of a quadratic function f(x) = ax2 + bx + c (a ≠ 0) is always a parabola.

true

The graph of every linear function of one variable is a straight line.

false

The line y = 0 has no slope.

false

The regression line associated with a collection of points always passes through at least one of them

false

The regression line associated with three data points (with different x-coordinates) always passes through all three points.

true

The regression line associated with two data points (with different x-coordinates) always passes through both points.

true

To find a linear function, all you need is a point and the slope


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