How do I graph these two problems?
y = −x2
g(x)= sqrt x-1
a good place to start would be here. Does your text not have any examples of graphing functions?
http://www.wolframalpha.com/input/?i=plot+y%3D-x%5E2%2C+y%3D%E2%88%9A%28x-1%29
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 equations y = −x^2 and g(x) = √(x-1), you can follow these steps:
1. Choose a range of x-values: Select a range of x-values that you want to plot on your graph. Consider both positive and negative values. For example, you might choose x-values from -5 to 5.
2. Calculate y-values for each x: Substitute each x-value into the equation and calculate the corresponding y-value. For example, if x = -2, y = -(-2)^2 = -4. Repeat this process for each x-value in your chosen range.
3. Plot the points: On a piece of graph paper or using graphing software, mark the coordinates for each (x, y) pair. For example, if x = -2, y = -4, then mark the point (-2, -4).
4. Connect the points: Once you have plotted all the points, connect them with a smooth line or curve. This represents the shape of the function.
5. Consider the domain and range: Pay attention to any restrictions or limitations on the domain and range specified in the equation. For example, the equation g(x) = √(x-1) has a restriction that x-1 must be greater than or equal to 0 (x ≥ 1) to avoid taking the square root of a negative number.
Using these steps, you can create the graph for each equation separately. The graph of y = −x^2 will be a downward-facing parabola, while the graph of g(x) = √(x-1) will be a half of a sideways U-shaped curve, only plotted for values of x greater than or equal to 1.