College Algebra CLEP Prep Practice Exam

Find the range of the function y = x2 - 4x + 3.

1. -1 ≤ y ≤ 3

2. y≥−1

3. 0 ≤ y ≤ 4

4. 3 ≤ y ≤ 7

The correct answer is: y≥−1

To determine the range of the function \( y = x^2 - 4x + 3 \), we first recognize that this is a quadratic function in standard form. The general form of a quadratic function is \( y = ax^2 + bx + c \), where \( a \) is positive, which means the parabola opens upwards. This indicates that the function has a minimum value at its vertex. To find the vertex, we can use the formula for the x-coordinate of the vertex, given by \( x = -\frac{b}{2a} \). In our function, \( a = 1 \) and \( b = -4 \). Therefore, \[ x = -\frac{-4}{2 \cdot 1} = \frac{4}{2} = 2. \] Next, we calculate the y-value of the function at this x-coordinate (the vertex): \[ y = (2)^2 - 4(2) + 3 = 4 - 8 + 3 = -1. \] Since the parabola opens upwards, this means that the minimum value of \( y \) is \( -1 \), which occurs when \( x =