Final answer:
The range of the function f(x) = 2x² - 8x + 7 is all real numbers greater than or equal to 1.
Step-by-step explanation:
The range of a function is the set of all possible output values. In this case, the function is f(x) = 2x² - 8x + 7. To find the range, we need to determine the minimum and maximum values that the function can take. Since the function is a quadratic, its graph is a parabola. The vertex of the parabola gives the minimum or maximum value, depending on whether the parabola opens upward or downward.
To find the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation. In this case, a = 2, b = -8, and c = 7. Plugging these values into the formula, we get x = -(-8)/(2*2) = 1. The y-coordinate of the vertex can be found by plugging x = 1 into the quadratic equation. So, f(1) = 2(1)² - 8(1) + 7 = 2 - 8 + 7 = 1.
Since the coefficient of x² is positive (2 > 0), the parabola opens upward, and the vertex is the minimum value. Therefore, the range of the function is all real numbers greater than or equal to 1.