sketch the graph y=abs(x)+2
then sketch over the y=x line.
The best to sketch graph if you don't know what the graph looks like is plug in points.
Sorry, we can't draw graphs for you here.
When x>0, y = x + 2
When x<0, y = -x + 2
Draw both parts of the curve. Two lines will join to form a notch at x=0, y = 2.
I assume you know how to plot y = x.
To sketch the graph of y = |x| + 2, you can follow these steps:
Step 1: Plot the vertex: The vertex of the graph is at (0, 2), since when x = 0, y = |0| + 2 = 2.
Step 2: Plot points symmetrically: To determine other points on the graph, you can choose values for x, compute the corresponding y-values, and plot the points. Since y = |x| + 2, you can take the absolute value of positive and negative x-values and add 2 to get the corresponding y-values. For example:
- When x = -2, y = |-2| + 2 = 4.
- When x = -1, y = |-1| + 2 = 3.
- When x = 1, y = |1| + 2 = 3.
- When x = 2, y = |2| + 2 = 4.
Plotting these points will give you a "V" shape, with the vertex at (0, 2) and the arms of the "V" extending to (2, 4) and (-2, 4), as well as (1, 3) and (-1, 3) on the line.
Step 3: Sketch the graph: Connect the plotted points smoothly to form the graph. The resulting graph is a V-shaped curve that opens upwards.
To sketch the line y = x, you can follow a similar process:
- Choose different x-values and compute the corresponding y-values by substituting each x-value into the equation.
- Plot these points and connect them to sketch the line.
The y = x line is a straight line that passes through the origin with a slope of 1, meaning that for every unit increase in x, there is a corresponding unit increase in y.
Sketching the y = x line over the graph of y = |x| + 2 will result in the line intersecting the "V" shape at the bottom point of the "V", and extending outwards in both directions.