Question

The function f(x) = (1/2) |x + 3| - 2. What is the domain and range? Axis of symmetry is at x=? Where is the vertex (x,y)? Where's the Y intercept? What's the value of a? What is the effect of a?

Answer 1

The domain of the function f(x) is all real numbers, the range is all real numbers greater than or equal to -2. The axis of symmetry is at x = -3, the vertex is at (-3, -2), and the y-intercept is -0.5. The value of a is 1/2 and it compresses the graph vertically by a factor of 2.

Step-by-step explanation:

The domain of the function f(x) = (1/2) |x + 3| - 2 is all real numbers since there are no restrictions on the input. The range of the function is all real numbers greater than or equal to -2, since the absolute value of x + 3 can never be negative. The axis of symmetry is at x = -3.

The vertex of the function is the point (-3, -2), since the axis of symmetry passes through the vertex. The y-intercept of the function can be found by plugging in x = 0. Therefore, f(0) = (1/2) |0 + 3| - 2 = (1/2) |3| - 2 = 1.5 - 2 = -0.5.

The value of a in the function is 1/2. The effect of a is to stretch or compress the graph vertically. In this case, the graph is compressed by a factor of 2.