10. consider the function $y = |x - 3|$. 10d graph the function.

Explanation:

Step1: Analyze the parent function

The parent function of absolute value is ( y = |x| ), which has a vertex at ( (0,0) ) and a V - shape opening upwards with slopes ( 1 ) (for ( x\geq0 )) and ( - 1 ) (for ( x < 0 )).

Step2: Determine the transformation

For the function ( y=|x - 3| ), we use the transformation rule for absolute value functions. The general form ( y=|x - h| ) represents a horizontal shift of the parent function ( y = |x| ). If ( h>0 ), the graph shifts ( h ) units to the right. Here, ( h = 3 ), so the graph of ( y = |x| ) shifts 3 units to the right.

Step3: Find the vertex

The vertex of ( y=|x - 3| ) is at ( (h,0)=(3,0) ).

Step4: Find two points on each ray

• For ( x\geq3 ), let's take ( x = 4 ), then ( y=|4 - 3|=1 ), so the point is ( (4,1) ). Let ( x = 5 ), then ( y=|5 - 3| = 2 ), so the point is ( (5,2) ).
• For ( x<3 ), let's take ( x = 2 ), then ( y=|2 - 3| = 1 ), so the point is ( (2,1) ). Let ( x=1 ), then ( y=|1 - 3|=2 ), so the point is ( (1,2) ).

Step5: Plot the vertex and the points and draw the graph

Plot the vertex ( (3,0) ), and the points ( (4,1),(5,2),(2,1),(1,2) ) etc. Then draw two rays: one with a slope of ( 1 ) for ( x\geq3 ) and one with a slope of ( - 1 ) for ( x < 3 ), forming a V - shape with the vertex at ( (3,0) ).

Answer:

The graph of ( y = |x - 3| ) is a V - shaped graph with vertex at ( (3,0) ), a ray with slope ( 1 ) for ( x\geq3 ) and a ray with slope ( - 1 ) for ( x < 3 ). (To draw it, plot the vertex ( (3,0) ) and points like ( (2,1),(4,1),(1,2),(5,2) ) and connect them appropriately.)