Final answer:
The graph of the quadratic function, y=f(x)=x²−16, is a parabola that opens upward with a vertex at (0, -16). Considering the given domain -3≤ x≤ 4, the values of y range from -16 (the value at the vertex) to 0. Hence, the range is -16 ≤ y ≤ 0.
Step-by-step explanation:
The function given is y=f(x)=x² −16. To find the range, we first need to see the behavior of the function. As this is a quadratic function, its graph is a parabola. Here, the parabola opens upward as the coefficient of x² is positive. Now, let's pinpoint the vertex of this parabola which is the lowest point for this type of parabola.
For the given function, the vertex happens at x=0 and y=-16 (you can find it by completing the square or using the vertex formula -b/2a for the x-coordinate and substituting it into the function to get the y-coordinate).
Now considering the domain -3≤ x≤ 4, we substitute these values into the function to find the corresponding y values:
- f(-3)=(-3)² -16 = 9-16 = -7
- f(4)= 4² -16 = 16 - 16 = 0
Therefore, the range of the function for the given domain is -16 ≤ y ≤ 0 since parabolas attain maximum/minimum at their vertex and -16 is the minimum value of the function.
Learn more about the Range of a Function