How do you graph # f(x) = 2abs x+1 #?

Question

Avery Alexander · Accepted Answer

When #x >= 0# we have #f(x) = 2abs(x) + 1 = 2x+1#, which is a straight line of slope #2#, starting from #(0, 1)# When #x <= 0# we have #f(x) = 2abs(x)+1 = -2x+1#, which is a straight line of slope #-2#, ending at #(0, 1)# So #f(x)# is basically a 'V' shape of slope #+-2# with vertex at #(0, 1)# graph{abs(2x)+1 [-10.04, 9.96, -2.24, 7.76]}

Eva Abramson · Answer

undefined To graph $ f(x) = 2| x + 1| $, follow these steps:

1. Identify the vertex:
   The vertex of the absolute value function $ |x| $ is at the point (0,0). However, in this case, there's a horizontal translation of 1 unit to the left due to the term $ x + 1 $. So, the vertex is at (-1, 0).

2. Determine the direction of the graph:
   The coefficient 2 in front of the absolute value function $ |x + 1| $ indicates a vertical stretch by a factor of 2.

3. Plot points to the left and right of the vertex:
   Choose a few x-values to the left and right of the vertex (-1, 0) and calculate the corresponding y-values.

4. Plot the points and draw the graph:
   Plot the points you calculated and connect them with a smooth curve. Ensure the graph extends indefinitely in both directions.

5. Label the graph:
   Label the axes and any key points if necessary.

By following these steps, you can graph the function $ f(x) = 2| x + 1| $.