Analyzing the domain and range of a function is really important when we're drawing graphs.
1. What is Domain?
The domain of a function is all the possible input values, or x-values, we can use. Knowing the domain helps us figure out which values to plot on the graph.
For example, the function ( f(x) = \sqrt{x} ) has a domain of ([0, \infty)). This means it can only use non-negative numbers (like 0 and positive numbers).
If we don't think about this, we might end up with confusing graphs.
2. What is Range?
The range is all the possible output values, or y-values, of a function. Understanding the range helps us know the limits on the vertical side of the graph.
For the function ( f(x) = x^2 ), the range is ([0, \infty)). This shows that the graph will never go below the x-axis.
3. Graph Features:
Intercepts: Knowing the domain and range makes it easier to find where the graph crosses the x and y axes.
Slope and Curvature: Looking at the slope and how the graph curves tells us if the function is going up or down.
By knowing the domain and range, students can draw accurate graphs that show how the function behaves. This helps them understand function characteristics better.
Analyzing the domain and range of a function is really important when we're drawing graphs.
1. What is Domain?
The domain of a function is all the possible input values, or x-values, we can use. Knowing the domain helps us figure out which values to plot on the graph.
For example, the function ( f(x) = \sqrt{x} ) has a domain of ([0, \infty)). This means it can only use non-negative numbers (like 0 and positive numbers).
If we don't think about this, we might end up with confusing graphs.
2. What is Range?
The range is all the possible output values, or y-values, of a function. Understanding the range helps us know the limits on the vertical side of the graph.
For the function ( f(x) = x^2 ), the range is ([0, \infty)). This shows that the graph will never go below the x-axis.
3. Graph Features:
Intercepts: Knowing the domain and range makes it easier to find where the graph crosses the x and y axes.
Slope and Curvature: Looking at the slope and how the graph curves tells us if the function is going up or down.
By knowing the domain and range, students can draw accurate graphs that show how the function behaves. This helps them understand function characteristics better.