Hey there!
a. To start, the domain of a function is the range of x values a graph has.
In the graph shown, you have a graph with x values that range from -4 to 0.
However, notice in the graph, there is a hole at the point (-4,6). This hole means that in the function, the domain value of -4 is not included in the domain.
Therefore, to represent your domain in interval notation, you would have:
(-4, 0]
**a parenthesis before a value signifies the value is not included (-4 is not included due to the hole) and a bracket signifies the value is included.
b. The range of a function is the range of y values the function has. Notice how the function's values range from -9 to 6, however there is a hole in the y value of 6 meaning it is not included. Therefore, your range should be [-9, 6).
c. To start, the x-intercept of a graph is the point in which the line passes through the x axis. In the graph shown, the line passes through the x axis at (-3,0). Therefore, your x-intercept would be (-3,0).
d. Similar to the x-intercept, the y-intercept of a graph is the point in which the line passes through the y-intercept. In the graph shown, the line passes through the y axis at (0,-9). Therefore, your y-intercept would be (0,-9).
e. To find the function value in the graph, first locate -2, the given value in f(-2), on the x-axis. Now, trace the point towards the line to find where the x values of -2 lies on the graph, which would be at point (-2,-5). Knowing this, f(-2) would be -5, the y value of the point.
Hope this helps and have a wonderful day! :)
