This is a little difficult...
Graph the Function
y=3 less than the absolute value of x+2
Obviously you cannot show me this on a graph, but I just need help with solving the equation...
Thanks!!!
http://www.jiskha.com/display.cgi?id=1447261918
To graph the function y = 3 less than the absolute value of x + 2, we can start by examining the equation. The absolute value function can be represented as |x|.
Step 1: First, consider the equation without the 3 subtraction: y = |x + 2|. This represents the absolute value of x + 2.
Step 2: Now, we need to shift the entire graph downward by 3 units since it is "3 less than" the absolute value. So the transformed equation becomes y = |x + 2| - 3.
Step 3: To plot the equation on a graph, we can create a table of values by choosing different values for x and calculating the corresponding values of y.
Let's choose a few values for x and calculate the corresponding y-values:
If x = -5, then y = |(-5) + 2| - 3 = 3 - 3 = 0.
If x = -2, then y = |(-2) + 2| - 3 = 0 - 3 = -3.
If x = 0, then y = |0 + 2| - 3 = 2 - 3 = -1.
If x = 2, then y = |2 + 2| - 3 = 4 - 3 = 1.
If x = 5, then y = |5 + 2| - 3 = 7 - 3 = 4.
Step 4: Plot the points (-5, 0), (-2, -3), (0, -1), (2, 1), and (5, 4) on the graph.
Step 5: Finally, connect the plotted points with a smooth curve. Since the absolute value function is symmetrical, the resulting graph will have a V-shape, with the vertex at (-2, -3) and the arms extending upward and downward.
That's it! You have successfully graphed the function y = 3 less than the absolute value of x + 2.
To graph the function y = 3 less than the absolute value of x + 2, we can start by understanding the behavior of the absolute value function.
The absolute value function, denoted as |x|, gives the distance of a number, x, from zero on a number line. This function always results in a non-negative value.
In the given function, y = 3 less than the absolute value of x + 2, we need to subtract 3 from the absolute value of x + 2. Let's break down the steps to solve this equation:
Step 1: Set up the equation: y = |x + 2| - 3.
Step 2: Replace y with 0 since we want to find the x-intercepts of the graph.
0 = |x + 2| - 3.
Step 3: Isolate the absolute value expression by adding 3 to both sides of the equation.
3 = |x + 2|.
Step 4: Break down the equation into two cases: positive and negative values.
Case 1: (x + 2) ≥ 0
In this case, the absolute value of (x + 2) will be the number itself.
3 = x + 2.
Solve for x:
x = 1.
Case 2: (x + 2) < 0
In this case, the absolute value of (x + 2) will be -(x + 2).
3 = -(x + 2).
Solve for x:
x = -5.
Step 5: Now that we have found the x-intercepts, we can plot these points on a graph.
The x-intercepts are x = 1 and x = -5.
The graph of the equation y = 3 less than the absolute value of x + 2 would have x-intercepts at x = 1 and x = -5. Since we don't have a specific y-value, we cannot determine any other points on the graph. However, we can still understand the behavior of the graph:
- The graph will be a 'V' shape, centered at x = -2.
- The vertex of the graph is at (-2, -3), which is 3 units down from the x-axis.
Note: Without a specific y-value, we cannot fully graph the function or provide a precise shape, but we can identify the key points and general characteristics of the graph.