Given the function
Graphing
a) According to the graph:
The graph of f opens down
The vertex of f is (0.5, -0.5)
The x-coordinate of the vertex is the equation of the axis of symmetry of the parabola. In this case, the vertex of the parabola is (0.5, -0.5). Therefore:
The axis of symmetry is x = 0.5
The y-intercept of a graph is the point where the graph crosses the y-axis. So,
Answer: A. The y-intercept is -1
The x-intercept of a graph is the point where the graph crosses the x-axis. In this case, we see that the graph does not cross the x-axis, so there is no x-intercept.
Answer: B. There is no x-intercept
b) The domain is the values of x. The range is the y values. Therefore:
The domain of f is (-∞, ∞)
The range of f is (-∞, -0.5]
c) -A function is increasing when as the value of the independent variable increases, the value of the function increases.
-A function is decreasing when, as the value of the independent variable increases, the value of the function decreases. So:
The function is increasing on the interval (-∞, 0.5)
The function is decreasing on the interval (0.5, ∞)
(1) down