This is the second part to my first question
A quadratic function
Graph the function g(x) = 4 − x2, and state the domain and range.
Solution
We plot enough points to get the correct shape of the graph.
See Fig. 11.10 for the graph. The domain is (−�‡, �‡). From the graph we see that the largest y-coordinate is 4. So the range is (−�‡, 4].
I can't paste the graph.
To graph the function g(x) = 4 - x^2, you can use the following steps:
1. Choose different values for x and calculate the corresponding values for g(x). For example, you can choose x = -2, -1, 0, 1, and 2.
When x = -2, g(-2) = 4 - (-2)^2 = 4 - 4 = 0.
When x = -1, g(-1) = 4 - (-1)^2 = 4 - 1 = 3.
When x = 0, g(0) = 4 - 0^2 = 4 - 0 = 4.
When x = 1, g(1) = 4 - (1)^2 = 4 - 1 = 3.
When x = 2, g(2) = 4 - (2)^2 = 4 - 4 = 0.
2. Plot these points on a graph. In this case, you would plot the points (-2, 0), (-1, 3), (0, 4), (1, 3), (2, 0).
3. Connect the points with a smooth curve to get the shape of the graph. It should open downwards since the coefficient of x^2 is negative.
The graph should resemble an upside-down "U" shape or a parabola that opens downward.
Regarding the domain and range:
- The domain of the function g(x) = 4 - x^2 is the set of all real numbers, which means there are no restrictions on the x-values. In interval notation, the domain is (-∞, ∞).
- From the graph, we can see that the highest point on the graph has a y-coordinate of 4. Therefore, the range of the function is from negative infinity (−∞) to 4, including 4. In interval notation, the range is (-∞, 4].
Please note that the graph is not in the text form, so it cannot be pasted here. But you can visualize it based on the information provided above.