Question

Постройте график функции y=(x^2-3x)/3-x и определите при каких значениях m прямая y=m не имеет общих точек с графиком????

Answer 1

Ответ: Прим m=-3 прямая y=m не имеет с графиков ни одной общей точки, т.к. в ОДЗ не входит значения (3;-3), ибо знаменатель не может быть равным 0.

Answer 2

Ответы на фотографии!

Answer 3

Graph of the Function y=(x^2-3x)/3-x

To determine the values of \( m \) for which the line \( y=m \) does not intersect the graph of the function \( y=\frac{x^2-3x}{3}-x \), we can analyze the properties of the function and the line.

The function \( y=\frac{x^2-3x}{3}-x \) can be rewritten as \( y=\frac{1}{3}x^2-x \).

The graph of the function \( y=\frac{1}{3}x^2-x \) is a parabola. To find the values of \( m \) for which the line \( y=m \) does not intersect the graph, we need to find the discriminant of the quadratic equation formed by setting the function equal to \( m \) and then analyze the discriminant.

Discriminant Analysis

The discriminant of a quadratic equation \( ax^2+bx+c=0 \) is given by the formula \( D=b^2-4ac \). When the discriminant is negative, the quadratic equation has no real roots, which means the line does not intersect the graph of the function.

For the function \( y=\frac{1}{3}x^2-x \), the discriminant is \( D=(-1)^2-4\left(\frac{1}{3}\right)(-m) \).

Determining the Values of m

To find the values of \( m \) for which the line \( y=m \) does not intersect the graph of the function, we need to solve the inequality \( D<0 \).

Substituting the discriminant into the inequality, we get \( (-1)^2-4\left(\frac{1}{3}\right)(-m)<0 \).

Solving this inequality will give us the range of values for \( m \) for which the line \( y=m \) does not intersect the graph of the function.

Conclusion

By solving the inequality \( (-1)^2-4\left(\frac{1}{3}\right)(-m)<0 \), we can determine the values of \( m \) for which the line \( y=m \) does not intersect the graph of the function \( y=\frac{1}{3}x^2-x \).