when I'm given a line graph and then a question of
For what value(s) of x is f(x) = 4
and
For what value(s) of x is f(x) = -4
how do I determine this?
Also, how do I tell the domain and range?
To determine the values of x for which f(x) = 4 and f(x) = -4, you would need to look at the line graph and find the points where the line intersects the y-axis at 4 and -4. The domain of the function is the set of all x-values for which the function is defined, and the range is the set of all y-values for which the function is defined.
To determine the value(s) of x for which f(x) equals a specific value (in this case, 4 or -4) from a given line graph, you need to look for the points on the graph that intersect the horizontal line corresponding to that specific value.
Here's a step-by-step approach to determine the value(s) of x when f(x) = 4 or f(x) = -4:
1. Identify the horizontal line on the graph that represents the value you want, whether it's 4 or -4. This line should be parallel to the x-axis and preferably distinct from any other lines on the graph.
2. Locate all the points where the line representing f(x) intersects the specific horizontal line. Mark these points on the graph.
3. Read the x-values of the marked points. These x-values represent the value(s) of x for which f(x) equals the specific value you are looking for.
For example, let's say you have a line graph, and there is a horizontal line at y = 4 that intersects the line representing f(x) at two points. The x-values of these intersection points would be the answer(s) to the question "For what value(s) of x is f(x) = 4?" Repeat the same steps to find the value(s) of x when f(x) = -4.
Determining the domain and range of a function from a line graph follows these steps:
1. Domain: Identify the x-values that the graph covers. The domain represents all the possible input values (x-values) for the function. In most cases, the domain is the range of x-values shown on the graph.
2. Range: Identify the y-values that the graph covers. The range represents all the possible output values (y-values) for the function. Find the lowest and highest y-values covered by the graph to determine the range.
By examining the x-values of the graph, you can identify the domain, while by examining the y-values, you can determine the range.
To determine the values of x for which f(x) equals 4 or -4 on a line graph, you need to find the point(s) where the graph intersects the corresponding y-values.
1. For f(x) = 4: Examine the line graph and locate the points where the line intersects the horizontal line y = 4. The x-coordinate(s) of these point(s) represent the value(s) of x for which f(x) = 4.
2. For f(x) = -4: Similarly, identify the points where the line intersects the horizontal line y = -4. These x-coordinate(s) correspond to the value(s) of x for which f(x) = -4.
Note: If the line graph intersects the given y-values at multiple points, there will be multiple values of x that satisfy the equation.
To determine the domain and range of a line graph:
- Domain refers to the set of all possible x-values for which the graph is defined. On a line graph, the domain is typically represented by the range of the x-axis.
- Range refers to the set of all possible y-values that the graph can take. On a line graph, the range is typically represented by the range of the y-axis.
By examining the extent of the line graph along the x-axis, you can determine the domain. Similarly, by examining the extent along the y-axis, you can identify the range.
Keep in mind that for a line graph, the domain and range can extend indefinitely or be limited based on the context of the problem or the given x and y-values.