graph the absolute value function and state its domain and range y=|x-1|+2
In google type:
functions graphs online
When you see list of results click on:
rechneronline.de/function-graphs/
When page be open in blue recatacangle type:
abs(x-1)+2
you will see graph
The domain of definition or simply the domain of a function is the set of "input" or argument values for which the function is defined.
Domain : All values of x
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
Range : y > = 2
When you type :
abs(x-1)+2
you must click option : Draw
To graph the absolute value function y = |x - 1| + 2, we can follow these steps:
Step 1: Identify the vertex of the absolute value function. In this case, the expression inside the absolute value brackets is x - 1. The vertex occurs when x - 1 = 0, so x = 1. Therefore, the vertex is at (1, 2).
Step 2: Determine which portion of the graph is positive and negative. When x < 1, the expression inside the absolute value brackets, x - 1, becomes negative, so the function overall is equal to -(x - 1) + 2. When x > 1, the expression inside the absolute value brackets, x - 1, becomes positive, so the function overall stays the same, y = x - 1 + 2.
Step 3: Plot the vertex on the coordinate plane, which is (1, 2).
Step 4: For x < 1, let's choose a few x-values to find their corresponding y-values. For example, when x = 0, the function becomes -(0 - 1) + 2 = 3. Similarly, when x = -1, the function becomes -(1 - 1) + 2 = 2. Plot these points on the graph.
Step 5: For x > 1, let's choose a few x-values again to find their corresponding y-values. For instance, when x = 2, the function becomes 2 - 1 + 2 = 3. Similarly, when x = 3, the function becomes 3 - 1 + 2 = 4. Plot these points on the graph.
Step 6: Draw a V-shaped graph connecting the points. The line will go downwards to the left of the vertex and upwards to the right of the vertex.
The graph of y = |x - 1| + 2 should be a V-shaped graph with the vertex at (1, 2).
Domain: The domain is all real numbers since there are no restrictions on the possible input values for x.
Range: The range is y ≥ 2, meaning the function's minimum value is 2 and can increase infinitely upwards.
To graph the absolute value function y = |x - 1| + 2, we can follow a step-by-step process:
Step 1: Determine the vertex of the absolute value function
- The vertex of the function y = |x - h| + k is given by (h, k)
- In this case, h = 1 and k = 2, so the vertex is (1, 2).
Step 2: Identify the slope
- The slope of the absolute value function is always 1 or -1.
Step 3: Plot the vertex and other key points
- Start by plotting the vertex, which is (1, 2).
- Choose a few more x-values on both sides of the vertex and calculate the corresponding y values using the equation y = |x - 1| + 2.
For example:
- When x = 0: y = |0 - 1| + 2 = 1 + 2 = 3
- When x = 2: y = |2 - 1| + 2 = 1 + 2 = 3
- When x = -1: y = |-1 - 1| + 2 = 2 + 2 = 4
Step 4: Connect the key points
- Draw a straight line segment between each point, making sure to maintain the shape of the absolute value function.
Now, let's discuss the domain and range of the function:
Domain:
- The domain of the function is the set of all real numbers.
- In this case, since there are no restrictions or exclusions in the equation y = |x - 1| + 2, the domain is (-∞, ∞).
Range:
- The range of the function is the set of all y-values that the function can produce.
- In this case, since the absolute value function y = |x - 1| + 2 always results in a positive value, the range is [2, ∞), meaning it includes all values greater than or equal to 2.
So, the graph of the absolute value function y = |x - 1| + 2 would be a V-shaped graph with the vertex at (1, 2), and its domain is (-∞, ∞) while the range is [2, ∞).