What parent function describes the set (-1, -1), (0, 0), (1, -1) (-2, -8), (2, -8)?
looks like
y = x^3 for x < 0 , y = -x^3 for x ≥ 0
to me
Looks like y = -|x^3| or y = -|x|^3
Not sure what the parent function would be. |x|^3 I guess, if all modifications to be considered are linear transformations.
To determine the parent function that describes a set of points, we need to analyze the pattern and identify any common characteristics. Let's examine the given set of points.
(-1, -1), (0, 0), (1, -1), (-2, -8), (2, -8)
First, notice that there are two different y-values: -1 and -8. Since we want to find a parent function that describes this set, we must consider a function that includes both of these y-values.
Next, let's look at the x-values. Notice that for each x-value, we have one corresponding y-value. This suggests that the function is not a quadratic equation (which would have two y-values for each x-value).
Now, let's focus on the y-values and see if we can identify a pattern. We have -1 followed by 0, then -1 again, and finally, we have two -8 values. Based on this pattern, it appears that the set represents a periodic function.
To find the equation of this periodic function, we need to identify the period and the midline.
The period represents the distance between two consecutive y-values that repeat. If we observe the pattern, we can see that the y-values repeat after every four points: (-1, -1), (0, 0), (1, -1), (-2, -8). Therefore, the period of this function is 4.
The midline represents the horizontal line around which the function oscillates. In this case, the y-values fluctuate between -1 and -8. To find the midline, we can average these two values: (-1 + -8) / 2 = -4.5.
Now that we have identified the period (4) and the midline (-4.5), we can write the equation of this periodic function.
A general form of a periodic function is y = A * f(B * x + C) + D, where A, B, C, and D are constants that determine specific characteristics of the function.
In our case, the midline is -4.5, which means D = -4.5. The pattern suggests that the function oscillates between -1 and -8, so the amplitude is given by |(-1 - (-8)) / 2| = 3.5. This gives us A = 3.5.
Since the period is 4, we can calculate B using the formula B = 2π / period. B = 2π / 4 = π / 2.
Thus, the equation of the parent function that describes the given set of points is:
y = 3.5 * sin(π / 2 * x) - 4.5
Therefore, the parent function that describes the set (-1, -1), (0, 0), (1, -1), (-2, -8), (2, -8) is y = 3.5 * sin(π / 2 * x) - 4.5.