Question

Consider continuous functions f, g, h, and k. Then complete the statements. Graph shows an upward parabola labeled f of x equals x squared minus 2x minus 6 with vertex at X-axis 1 and Y-axis minus 7. The parabola goes through (minus 2, 2) and (4, 2). Function h is two times the square of the difference of x and 1. Select the correct answer from each drop-down. The function that has the least minimum value is function . The function that has the greatest minimum value is function .

Answer 1

Function h has the least minimum value of 0, while function f has the greatest minimum value of -7.

Step-by-step explanation:

The function that has the least minimum value is function h. Function h is two times the square of the difference of x and 1. Since it is a square, the function will never have negative values, and because it is multiplied by 2, it will always be larger than 0. Therefore, the minimum value of function h is 0.

The function that has the greatest minimum value is function f. The given graph of f(x) = x² - 2x - 6 is an upward parabola with a vertex at (1, -7). Since the vertex is the minimum point of the parabola, the minimum value of function f is -7.