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.
Yes that's right. `u`
Domain is all real numbers or (-infinity, +infinity). And range is (-infinity, 4] since the highest value of g(x) occurs when x^2 is zero.
Yes, the graph is a parabola with a maximum (its vertex) which is at point (0,4)
To graph the function g(x) = 4 - x^2, you can follow these steps:
Step 1: Make a table of x and y values. Choose a few values for x and calculate their corresponding y values using the function. For example, you can choose x values of -3, -2, -1, 0, 1, 2, and 3.
Step 2: Plot the points on a coordinate plane. Assign the x values to the x-axis and the y values to the y-axis. Connect the points to form a smooth curve.
Step 3: Based on the graph, determine the domain and range:
- The domain is the set of all possible x values for which the function is defined. In this case, the domain is (-∞, ∞), as there are no restrictions on the x values.
- The range is the set of all possible y values the function can take. From the graph, it can be observed that the largest y-coordinate is 4, and the curve extends downwards towards negative infinity. Therefore, the range is (-∞, 4].
Note: As you mentioned, you are unable to provide the graph. However, knowing the general shape of a quadratic graph (a downward-opening parabola), you can still determine the domain and range.