Quick Check # 1 Solutions (Odd Degree Polynomials)
1) When the leading coefficient is positive
2) When the leading coefficient is negative
3) At even powered factors, the graph just touches the x-axis at the x-intercept and goes back in the same direction (it “bounces” or is tangent to the x-axis at the point). The y-values will not change sign on opposite sides of the x-intercept.
4) At odd powered factors, the graph crosses the x-axis at the x-intercept. The y- values will change sign on opposite sides of the x-intercept.
5) The number of turns the function makes is at most the degree of the function minus one. In other words, the number of turns plus one will give you the smallest degree of the function.
1) When the leading coefficient is positive
- As \(x\) approaches positive infinity, \(y\) approaches positive infinity
- As \(x\) approaches negative infinity, \(y\) approaches negative infinity
2) When the leading coefficient is negative
- As \(x\) approaches positive infinity, \(y\) approaches negative infinity
- As \(x\) approaches negative infinity, \(y\) approaches positive infinity
3) At even powered factors, the graph just touches the x-axis at the x-intercept and goes back in the same direction (it “bounces” or is tangent to the x-axis at the point). The y-values will not change sign on opposite sides of the x-intercept.
4) At odd powered factors, the graph crosses the x-axis at the x-intercept. The y- values will change sign on opposite sides of the x-intercept.
5) The number of turns the function makes is at most the degree of the function minus one. In other words, the number of turns plus one will give you the smallest degree of the function.