Which of the following functions has a maximum y value of 4?

To find the function with a maximum y value of 4, we need to analyze the given options. Let's consider each function one by one and determine their maximum y values.

1. f(x) = 2x + 3 To find the maximum value of this linear function, we need to determine if it has an upper bound. However, since the coefficient of x is positive, the function will continue to increase indefinitely as x increases. Therefore, this function does not have a maximum y value of 4.

2. g(x) = x^2 + 4 This is a quadratic function in the form of a parabola. The coefficient of x^2 is positive, indicating that the parabola opens upwards. To find the maximum value, we can determine the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a and b are the coefficients of x^2 and x, respectively. In this case, a = 1 and b = 0, so the x-coordinate of the vertex is x = 0. Substituting this value into the function, we get g(0) = 0^2 + 4 = 4. Therefore, this function has a maximum y value of 4.

3. h(x) = 4 - x This is a linear function with a negative coefficient of x. As x increases, the function will decrease. However, since the coefficient of x is negative, the function will continue to decrease indefinitely as x increases. Therefore, this function does not have a maximum y value of 4.

Based on our analysis, the function g(x) = x^2 + 4 has a maximum y value of 4.