Enter your answer and show all the steps that you use to solve this problem in the space provided. Write an inequality for the graph. The answer is y=|5-x|+1
To write an inequality for the graph y = |5-x| + 1, we need to understand the properties of absolute value.
For any real number x, the absolute value of x (denoted as |x|) is defined as the distance of x from 0 on the number line. This means that if x is positive or negative, |x| will always be positive.
In this case, the expression |5-x| represents the distance of (5-x) from 0. The value of (5-x) can be positive or negative, but the absolute value will always be positive.
Adding 1 to the absolute value gives us |5-x| + 1, which shifts the graph of |5-x| one unit upward.
Therefore, the inequality for the given graph is y ≥ 1. This means that y is greater than or equal to 1.
Alternatively, if you want to write the inequality in terms of x, you can isolate x in the equation y = |5-x| + 1:
1. Subtract 1 from both sides: y - 1 = |5-x|
2. Remove the absolute value by considering both cases of (5-x):
a. If 5-x is positive or zero, then |5-x| = 5-x. So the equation becomes y - 1 = 5-x.
b. If 5-x is negative, then |5-x| = -(5-x) = x-5. So the equation becomes y - 1 = x-5.
3. Rearrange the equations to solve for x:
a. If 5-x is positive or zero: y - 1 = 5-x
--> x - y = -4
b. If 5-x is negative: y - 1 = x-5
--> -x - y = -4
4. The inequality for the graph is either x - y ≥ -4 or -x - y ≥ -4 (depending on the value of 5-x).
Thus, the inequality for the graph is x - y ≥ -4 or -x - y ≥ -4.
To write an inequality for the given graph, we need to understand what the graph represents.
The equation y = |5-x| + 1 represents the equation of a graph that is a V-shaped absolute value function.
To write the inequality, we need to consider two cases:
Case 1: When (5-x) is greater than or equal to 0.
In this case, the absolute value will be equal to the value inside the absolute value function.
So, when (5-x) is greater than or equal to 0, the inequality will be:
y = 5-x + 1
Simplifying the above equation:
y = 6 - x
Case 2: When (5-x) is less than 0.
In this case, the absolute value will be equal to the negation of the value inside the absolute value function.
So, when (5-x) is less than 0, the inequality will be:
y = -(5-x) + 1
Simplifying the above equation:
y = x - 4
Combining both cases, the inequality for the graph is:
y = 6 - x, when x is greater than or equal to 5
y = x - 4, when x is less than 5
To write an inequality for the graph, we need to understand the equation y = |5-x| + 1.
In this equation, |5-x| represents the absolute value of the expression (5-x). Absolute value is a function that returns the positive value of any number, so regardless of whether (5-x) is positive or negative, the absolute value will always be positive.
The expression (5-x) determines the horizontal shift of the graph. If (5-x) is positive, the graph will shift to the right, and if (5-x) is negative, the graph will shift to the left.
Finally, adding 1 to the absolute value function shifts the graph vertically upward by 1 unit.
Now, let's start writing the inequality for the graph.
Step 1: Identify the direction of the inequality based on the graph.
In this case, the absolute value will always be positive or zero, so the graph will always be greater than or equal to 1.
Step 2: Write the inequality by replacing y with the equation.
Since the graph is greater than or equal to 1, the inequality is:
y ≥ |5-x| + 1
And that's how you write the inequality for the given graph.