How do i solve the functions domain, range, x intercept and y intercept for this function..there is a a shaded dot on (-4,-4) and then theres a curved line going up to an unshaded dot on (0,0), it also has to be interval notation but im not sure how to do that either. thanks
To solve for the domain, range, x-intercept, and y-intercept of a function, we need to analyze the given information and the graph.
1. Domain: The domain of a function is the set of all possible input values (x-values) for which the function is defined. To find the domain, we look for any restrictions on the x-values based on the graph or the function itself.
In this case, since there are no specific restrictions mentioned and the graph seems to continue indefinitely in both directions, we can assume that the domain is all real numbers. Therefore, the domain is (-∞, +∞) in interval notation.
2. Range: The range of a function is the set of all possible output values (y-values) that the function can produce. To determine the range, we look at the vertical extent of the graph.
Looking at the graph, we can observe that the shaded dot at (-4, -4) falls on the curve, and the unshaded dot at (0, 0) lies on the curved line. Based on this, we can infer that the y-values are at least as low as -4 and increase as the points move upwards on the curve. Therefore, the range is (-4, +∞) in interval notation.
3. x-intercept: The x-intercept(s) of a function is/are the point(s) at which the graph intersects the x-axis. In other words, the x-intercept is the value(s) of x for which the corresponding y-value is zero.
Since the graph passes through the point (0, 0) on the x-axis, this means that there is only one x-intercept at x = 0.
4. y-intercept: The y-intercept is the point at which the graph intersects the y-axis. In other words, it is the point where the x-value is zero.
Since the graph passes through the point (0, 0), this means that the y-intercept is at y = 0.
In summary:
- Domain: (-∞, +∞) in interval notation
- Range: (-4, +∞) in interval notation
- X-intercept: x = 0
- Y-intercept: y = 0