True/False Math 123 Functions + Linear Models
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