I really need help on this question

9514 1404 393

Step-by-step explanation:

The general shape of "up to the right" tells you this is an odd-degree polynomial with a positive leading coefficient. As such, the value of f(x) will have the same sign as the value of x when x gets large. The end behavior could be described by ...

  lim[x → -∞] f(x) → -∞

  lim[x → ∞] f(x) → ∞

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The curve crosses the x-axis 3 times and touches it once without crossing. Each crossing is a real zero. Each touch is a a real zero with an even multiplicity. The shape (flatness) of the touch gives a clue as to the multiplicity. (Flatter means higher multiplicity.) Here the shape indicates the zero has a multiplicity of 2.

So, there are 4 distinct real zeros, one with a multiplicity of 2, for a total of 5 real zeros.

Additional comment

An even-degree polynomial function has a generally U shape. If the leading coefficient is negative, the U is upside down: ∩. An even-degree polynomial will have the limits of f(x) having the same sign, regardless of the sign of x.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: