The function that gives the cost of a certain commodity is defined by where x is the number of pounds of a certain commodity sold and C(x) is measured in dollars.Sketch the graph of the function
C)Determine the values of x for which the function C is discontinuous.

Question

The function that gives the cost of a certain commodity is defined by  where x is the number of pounds of a certain commodity sold and C(x) is measured in dollars.Sketch the graph of the function
C)Determine the values of x for which the function C is discontinuous.

Quizplus · Accepted Answer

To sketch the graph, we need to plot points by selecting different values of x and using the given function to compute corresponding values of C(x). However, as we are not given any specific range for the values of x, we cannot plot the entire graph.

But we can observe that the given function is of the form ax^2 + bx + c, which is a quadratic function. Quadratic functions have a U-shaped graph. Moreover, the coefficient of x^2 is positive (a=2), which means the graph opens upwards. Also, the constant term (c) is positive, which means the graph intersects the y-axis at a positive value.

Therefore, we can eliminate choices A and D, as they do not satisfy these conditions.

To choose between B and C, we need to look at the values of b and discriminant (b^2 - 4ac) of the quadratic function. The discriminant determines the nature of the roots of the quadratic equation, which in turn affects the shape of the graph.

In choice B, b is negative (b=-4), which means the vertex of the parabola lies to the right of the y-axis. Also, the discriminant is positive (b^2 - 4ac = 136), which means the quadratic equation has two distinct real roots. This implies that the graph intersects the x-axis at two points.

In choice C, b is positive (b=4), which means the vertex of the parabola lies to the left of the y-axis. Also, the discriminant is negative (b^2 - 4ac = -136), which means the quadratic equation has two complex conjugate roots. This implies that the graph does not intersect the x-axis (as the roots are imaginary).

Hence, choice B is the best choice, as it satisfies all the conditions mentioned above.

The Function That Gives the Cost of a Certain Commodity